- Introduction
- 1.1 Use the Language of Algebra
- 1.2 Integers
- 1.3 Fractions
- 1.4 Decimals
- 1.5 Properties of Real Numbers
- Key Concepts
Review Exercises
Practice test.
- 2.1 Use a General Strategy to Solve Linear Equations
- 2.2 Use a Problem Solving Strategy
- 2.3 Solve a Formula for a Specific Variable
- 2.4 Solve Mixture and Uniform Motion Applications
- 2.5 Solve Linear Inequalities
- 2.6 Solve Compound Inequalities
- 2.7 Solve Absolute Value Inequalities
- 3.1 Graph Linear Equations in Two Variables
- 3.2 Slope of a Line
- 3.3 Find the Equation of a Line
- 3.4 Graph Linear Inequalities in Two Variables
- 3.5 Relations and Functions
- 3.6 Graphs of Functions
- 4.1 Solve Systems of Linear Equations with Two Variables
- 4.2 Solve Applications with Systems of Equations
- 4.3 Solve Mixture Applications with Systems of Equations
- 4.4 Solve Systems of Equations with Three Variables
- 4.5 Solve Systems of Equations Using Matrices
- 4.6 Solve Systems of Equations Using Determinants
- 4.7 Graphing Systems of Linear Inequalities
- 5.1 Add and Subtract Polynomials
- 5.2 Properties of Exponents and Scientific Notation
- 5.3 Multiply Polynomials
- 5.4 Dividing Polynomials
- Introduction to Factoring
- 6.1 Greatest Common Factor and Factor by Grouping
- 6.2 Factor Trinomials
- 6.3 Factor Special Products
- 6.4 General Strategy for Factoring Polynomials
- 6.5 Polynomial Equations
- 7.1 Multiply and Divide Rational Expressions
- 7.2 Add and Subtract Rational Expressions
- 7.3 Simplify Complex Rational Expressions
- 7.4 Solve Rational Equations
- 7.5 Solve Applications with Rational Equations
- 7.6 Solve Rational Inequalities
- 8.1 Simplify Expressions with Roots
- 8.2 Simplify Radical Expressions
- 8.3 Simplify Rational Exponents
- 8.4 Add, Subtract, and Multiply Radical Expressions
- 8.5 Divide Radical Expressions
- 8.6 Solve Radical Equations
- 8.7 Use Radicals in Functions
- 8.8 Use the Complex Number System
- 9.1 Solve Quadratic Equations Using the Square Root Property
- 9.2 Solve Quadratic Equations by Completing the Square
- 9.3 Solve Quadratic Equations Using the Quadratic Formula
- 9.4 Solve Quadratic Equations in Quadratic Form
- 9.5 Solve Applications of Quadratic Equations
- 9.6 Graph Quadratic Functions Using Properties
- 9.7 Graph Quadratic Functions Using Transformations
- 9.8 Solve Quadratic Inequalities
- 10.1 Finding Composite and Inverse Functions
- 10.2 Evaluate and Graph Exponential Functions
- 10.3 Evaluate and Graph Logarithmic Functions
- 10.4 Use the Properties of Logarithms
- 10.5 Solve Exponential and Logarithmic Equations
- 11.1 Distance and Midpoint Formulas; Circles
- 11.2 Parabolas
- 11.3 Ellipses
- 11.4 Hyperbolas
- 11.5 Solve Systems of Nonlinear Equations
- 12.1 Sequences
- 12.2 Arithmetic Sequences
- 12.3 Geometric Sequences and Series
- 12.4 Binomial Theorem
x = 4 3 , x = −4 3 x = 4 3 , x = −4 3
y = 3 3 , y = −3 3 y = 3 3 , y = −3 3
x = 7 , x = −7 x = 7 , x = −7
m = 4 , m = −4 m = 4 , m = −4
c = 2 3 i , c = −2 3 i c = 2 3 i , c = −2 3 i
c = 2 6 i , c = −2 6 i c = 2 6 i , c = −2 6 i
x = 2 10 , x = −2 10 x = 2 10 , x = −2 10
y = 2 7 , y = −2 7 y = 2 7 , y = −2 7
r = 6 5 5 , r = − 6 5 5 r = 6 5 5 , r = − 6 5 5
t = 8 3 3 , t = − 8 3 3 t = 8 3 3 , t = − 8 3 3
a = 3 + 3 2 , a = 3 − 3 2 a = 3 + 3 2 , a = 3 − 3 2
b = −2 + 2 10 , b = −2 − 2 10 b = −2 + 2 10 , b = −2 − 2 10
x = 1 2 + 5 2 x = 1 2 + 5 2 , x = 1 2 − 5 2 x = 1 2 − 5 2
y = − 3 4 + 7 4 , y = − 3 4 − 7 4 y = − 3 4 + 7 4 , y = − 3 4 − 7 4
a = 5 + 2 5 , a = 5 − 2 5 a = 5 + 2 5 , a = 5 − 2 5
b = −3 + 4 2 , b = −3 − 4 2 b = −3 + 4 2 , b = −3 − 4 2
r = − 4 3 + 2 2 i 3 , r = − 4 3 − 2 2 i 3 r = − 4 3 + 2 2 i 3 , r = − 4 3 − 2 2 i 3
t = 4 + 10 i 2 , t = 4 − 10 i 2 t = 4 + 10 i 2 , t = 4 − 10 i 2
m = 7 3 , m = −1 m = 7 3 , m = −1
n = − 3 4 , n = − 7 4 n = − 3 4 , n = − 7 4
ⓐ ( a − 10 ) 2 ( a − 10 ) 2 ⓑ ( b − 5 2 ) 2 ( b − 5 2 ) 2 ⓒ ( p + 1 8 ) 2 ( p + 1 8 ) 2
ⓐ ( b − 2 ) 2 ( b − 2 ) 2 ⓑ ( n + 13 2 ) 2 ( n + 13 2 ) 2 ⓒ ( q − 1 3 ) 2 ( q − 1 3 ) 2
x = −5 , x = −1 x = −5 , x = −1
y = 1 , y = 9 y = 1 , y = 9
y = 5 + 15 i , y = 5 − 15 i y = 5 + 15 i , y = 5 − 15 i
z = −4 + 3 i , z = −4 − 3 i z = −4 + 3 i , z = −4 − 3 i
x = 8 + 4 3 , x = 8 − 4 3 x = 8 + 4 3 , x = 8 − 4 3
y = −4 + 3 3 , y = −4 − 3 3 y = −4 + 3 3 , y = −4 − 3 3
a = −7 , a = 3 a = −7 , a = 3
b = −10 , b = 2 b = −10 , b = 2
p = 5 2 + 61 2 , p = 5 2 − 61 2 p = 5 2 + 61 2 , p = 5 2 − 61 2
q = 7 2 + 37 2 , q = 7 2 − 37 2 q = 7 2 + 37 2 , q = 7 2 − 37 2
c = −9 , c = 3 c = −9 , c = 3
d = 11 , d = −7 d = 11 , d = −7
m = −7 , m = −1 m = −7 , m = −1
n = −2 , n = 8 n = −2 , n = 8
r = − 7 3 , r = 3 r = − 7 3 , r = 3
t = − 5 2 , t = 2 t = − 5 2 , t = 2
x = − 3 8 + 41 8 , x = − 3 8 − 41 8 x = − 3 8 + 41 8 , x = − 3 8 − 41 8
y = 5 3 + 10 3 , y = 5 3 − 10 3 y = 5 3 + 10 3 , y = 5 3 − 10 3
y = 1 , y = 2 3 y = 1 , y = 2 3
z = 1 , z = − 3 2 z = 1 , z = − 3 2
a = −3 , a = 5 a = −3 , a = 5
b = −6 , b = −4 b = −6 , b = −4
m = −6 + 15 3 , m = −6 − 15 3 m = −6 + 15 3 , m = −6 − 15 3
n = −2 + 2 6 5 , n = −2 − 2 6 5 n = −2 + 2 6 5 , n = −2 − 2 6 5
a = 1 4 + 31 4 i , a = 1 4 − 31 4 i a = 1 4 + 31 4 i , a = 1 4 − 31 4 i
b = − 1 5 + 19 5 i , b = − 1 5 − 19 5 i b = − 1 5 + 19 5 i , b = − 1 5 − 19 5 i
x = −1 + 6 , x = −1 − 6 x = −1 + 6 , x = −1 − 6
y = 1 + 2 , y = 1 − 2 y = 1 + 2 , y = 1 − 2
c = 2 + 7 3 , c = 2 − 7 3 c = 2 + 7 3 , c = 2 − 7 3
d = 9 + 33 4 , d = 9 − 33 4 d = 9 + 33 4 , d = 9 − 33 4
r = −5 r = −5
t = 4 5 t = 4 5
ⓐ 2 complex solutions; ⓑ 2 real solutions; ⓒ 1 real solution
ⓐ 2 real solutions; ⓑ 2 complex solutions; ⓒ 1 real solution
ⓐ factoring; ⓑ Square Root Property; ⓒ Quadratic Formula
ⓐ Quadratic Forumula; ⓑ Factoring or Square Root Property ⓒ Square Root Property
x = 2 , x = − 2 , x = 2 , x = −2 x = 2 , x = − 2 , x = 2 , x = −2
x = 7 , x = − 7 , x = 2 , x = −2 x = 7 , x = − 7 , x = 2 , x = −2
x = 3 , x = 1 x = 3 , x = 1
y = −1 , y = 1 y = −1 , y = 1
x = 9 , x = 16 x = 9 , x = 16
x = 4 , x = 16 x = 4 , x = 16
x = −8 , x = 343 x = −8 , x = 343
x = 81 , x = 625 x = 81 , x = 625
x = 4 3 x = 2 x = 4 3 x = 2
x = 2 5 , x = 3 4 x = 2 5 , x = 3 4
The two consecutive odd integers whose product is 99 are 9, 11, and −9, −11
The two consecutive even integers whose product is 128 are 12, 14 and −12, −14.
The height of the triangle is 12 inches and the base is 76 inches.
The height of the triangle is 11 feet and the base is 20 feet.
The length of the garden is approximately 18 feet and the width 11 feet.
The length of the tablecloth is approximatel 11.8 feet and the width 6.8 feet.
The length of the flag pole’s shadow is approximately 6.3 feet and the height of the flag pole is 18.9 feet.
The distance between the opposite corners is approximately 7.2 feet.
The arrow will reach 180 feet on its way up after 3 seconds and again on its way down after approximately 3.8 seconds.
The ball will reach 48 feet on its way up after approximately .6 second and again on its way down after approximately 5.4 seconds.
The speed of the jet stream was 100 mph.
The speed of the jet stream was 50 mph.
Press #1 would take 12 hours, and Press #2 would take 6 hours to do the job alone.
The red hose take 6 hours and the green hose take 3 hours alone.
ⓐ up; ⓑ down
ⓐ down; ⓑ up
ⓐ x = 2 ; x = 2 ; ⓑ ( 2 , −7 ) ( 2 , −7 )
ⓐ x = 1 ; x = 1 ; ⓑ ( 1 , −5 ) ( 1 , −5 )
y -intercept: ( 0 , −8 ) ( 0 , −8 ) x -intercepts ( −4 , 0 ) , ( 2 , 0 ) ( −4 , 0 ) , ( 2 , 0 )
y -intercept: ( 0 , −12 ) ( 0 , −12 ) x -intercepts ( −2 , 0 ) , ( 6 , 0 ) ( −2 , 0 ) , ( 6 , 0 )
y -intercept: ( 0 , 4 ) ( 0 , 4 ) no x -intercept
y -intercept: ( 0 , −5 ) ( 0 , −5 ) x -intercepts ( −1 , 0 ) , ( 5 , 0 ) ( −1 , 0 ) , ( 5 , 0 )
The minimum value of the quadratic function is −4 and it occurs when x = 4.
The maximum value of the quadratic function is 5 and it occurs when x = 2.
It will take 4 seconds for the stone to reach its maximum height of 288 feet.
It will 6.5 seconds for the rocket to reach its maximum height of 676 feet.
ⓑ The graph of g ( x ) = x 2 + 1 g ( x ) = x 2 + 1 is the same as the graph of f ( x ) = x 2 f ( x ) = x 2 but shifted up 1 unit. The graph of h ( x ) = x 2 − 1 h ( x ) = x 2 − 1 is the same as the graph of f ( x ) = x 2 f ( x ) = x 2 but shifted down 1 unit.
ⓑ The graph of h ( x ) = x 2 + 6 h ( x ) = x 2 + 6 is the same as the graph of f ( x ) = x 2 f ( x ) = x 2 but shifted up 6 units. The graph of h ( x ) = x 2 − 6 h ( x ) = x 2 − 6 is the same as the graph of f ( x ) = x 2 f ( x ) = x 2 but shifted down 6 units.
ⓑ The graph of g ( x ) = ( x + 2 ) 2 g ( x ) = ( x + 2 ) 2 is the same as the graph of f ( x ) = x 2 f ( x ) = x 2 but shifted left 2 units. The graph of h ( x ) = ( x − 2 ) 2 h ( x ) = ( x − 2 ) 2 is the same as the graph of f ( x ) = x 2 f ( x ) = x 2 but shift right 2 units.
ⓑ The graph of g ( x ) = ( x + 5 ) 2 g ( x ) = ( x + 5 ) 2 is the same as the graph of f ( x ) = x 2 f ( x ) = x 2 but shifted left 5 units. The graph of h ( x ) = ( x − 5 ) 2 h ( x ) = ( x − 5 ) 2 is the same as the graph of f ( x ) = x 2 f ( x ) = x 2 but shifted right 5 units.
f ( x ) = −4 ( x + 1 ) 2 + 5 f ( x ) = −4 ( x + 1 ) 2 + 5
f ( x ) = 2 ( x − 2 ) 2 − 5 f ( x ) = 2 ( x − 2 ) 2 − 5
ⓐ f ( x ) = 3 ( x − 1 ) 2 + 2 f ( x ) = 3 ( x − 1 ) 2 + 2 ⓑ
ⓐ f ( x ) = −2 ( x − 2 ) 2 + 1 f ( x ) = −2 ( x − 2 ) 2 + 1 ⓑ
f ( x ) = ( x − 3 ) 2 − 4 f ( x ) = ( x − 3 ) 2 − 4
f ( x ) = ( x + 3 ) 2 − 1 f ( x ) = ( x + 3 ) 2 − 1
ⓑ ( −4 , −2 ) ( −4 , −2 )
ⓑ ( − ∞ , 2 ] ∪ [ 6 , ∞ ) ( − ∞ , 2 ] ∪ [ 6 , ∞ )
ⓑ ( −1 , 5 ) ( −1 , 5 )
ⓑ ( − ∞ , 2 ] ∪ [ 8 , ∞ ) ( − ∞ , 2 ] ∪ [ 8 , ∞ )
( − ∞ , −4 ] ∪ [ 2 , ∞ ) ( − ∞ , −4 ] ∪ [ 2 , ∞ )
[ −3 , 5 ] [ −3 , 5 ]
[ −1 − 2 , −1 + 2 ] [ −1 − 2 , −1 + 2 ]
( − ∞ , 4 − 2 ) ∪ ( 4 + 2 , ∞ ) ( − ∞ , 4 − 2 ) ∪ ( 4 + 2 , ∞ )
ⓐ ( − ∞ , ∞ ) ( − ∞ , ∞ ) ⓑ no solution
ⓐ no solution ⓑ ( − ∞ , ∞ ) ( − ∞ , ∞ )
Section 9.1 Exercises
a = ± 7 a = ± 7
r = ± 2 6 r = ± 2 6
u = ± 10 3 u = ± 10 3
m = ± 3 m = ± 3
x = ± 6 x = ± 6
x = ± 5 i x = ± 5 i
x = ± 3 7 i x = ± 3 7 i
x = ± 9 x = ± 9
a = ± 2 5 a = ± 2 5
p = ± 4 7 7 p = ± 4 7 7
y = ± 4 10 5 y = ± 4 10 5
u = 14 , u = −2 u = 14 , u = −2
m = 6 ± 2 5 m = 6 ± 2 5
r = 1 2 ± 3 2 r = 1 2 ± 3 2
y = − 2 3 ± 2 2 9 y = − 2 3 ± 2 2 9
a = 7 ± 5 2 a = 7 ± 5 2
x = −3 ± 2 2 x = −3 ± 2 2
c = − 1 5 ± 3 3 5 i c = − 1 5 ± 3 3 5 i
x = 3 4 ± 7 2 i x = 3 4 ± 7 2 i
m = 2 ± 2 2 m = 2 ± 2 2
x = 3 + 2 3 , x = 3 − 2 3 x = 3 + 2 3 , x = 3 − 2 3
x = − 3 5 , x = 9 5 x = − 3 5 , x = 9 5
x = − 7 6 , x = 11 6 x = − 7 6 , x = 11 6
r = ± 4 r = ± 4
a = 4 ± 2 7 a = 4 ± 2 7
w = 1 , w = 5 3 w = 1 , w = 5 3
a = ± 3 2 a = ± 3 2
p = 1 3 ± 7 3 p = 1 3 ± 7 3
m = ± 2 2 i m = ± 2 2 i
u = 7 ± 6 2 u = 7 ± 6 2
m = 4 ± 2 3 m = 4 ± 2 3
x = −3 , x = −7 x = −3 , x = −7
c = ± 5 6 6 c = ± 5 6 6
x = 6 ± 2 i x = 6 ± 2 i
Answers will vary.
Section 9.2 Exercises
ⓐ ( m − 12 ) 2 ( m − 12 ) 2 ⓑ ( x − 11 2 ) 2 ( x − 11 2 ) 2 ⓒ ( p − 1 6 ) 2 ( p − 1 6 ) 2
ⓐ ( p − 11 ) 2 ( p − 11 ) 2 ⓑ ( y + 5 2 ) 2 ( y + 5 2 ) 2 ⓒ ( m + 1 5 ) 2 ( m + 1 5 ) 2
u = −3 , u = 1 u = −3 , u = 1
x = −1 , x = 21 x = −1 , x = 21
m = −2 ± 2 10 i m = −2 ± 2 10 i
r = −3 ± 2 i r = −3 ± 2 i
a = 5 ± 2 5 a = 5 ± 2 5
x = − 5 2 ± 33 2 x = − 5 2 ± 33 2
u = 1 , u = 13 u = 1 , u = 13
r = −2 , r = 6 r = −2 , r = 6
v = 9 2 ± 89 2 v = 9 2 ± 89 2
x = 5 ± 30 x = 5 ± 30
x = −7 , x = 3 x = −7 , x = 3
m = −11 , m = 1 m = −11 , m = 1
n = 1 ± 14 n = 1 ± 14
c = −2 , c = 3 2 c = −2 , c = 3 2
x = −5 , x = 3 2 x = −5 , x = 3 2
p = − 7 4 ± 161 4 p = − 7 4 ± 161 4
x = 3 10 ± 191 10 i x = 3 10 ± 191 10 i
Section 9.3 Exercises
m = −1 , m = 3 4 m = −1 , m = 3 4
p = 1 2 , p = 3 p = 1 2 , p = 3
p = −4 , p = −3 p = −4 , p = −3
r = −3 , r = 11 r = −3 , r = 11
u = −7 ± 73 6 u = −7 ± 73 6
a = 3 ± 3 2 a = 3 ± 3 2
x = −4 ± 2 5 x = −4 ± 2 5
y = −2 , y = 1 3 y = −2 , y = 1 3
x = − 3 4 ± 15 4 i x = − 3 4 ± 15 4 i
x = 3 8 ± 7 8 i x = 3 8 ± 7 8 i
v = 2 ± 2 13 v = 2 ± 2 13
y = −4 , y = 7 y = −4 , y = 7
b = −2 ± 11 6 b = −2 ± 11 6
c = − 3 4 c = − 3 4
q = − 3 5 q = − 3 5
ⓐ no real solutions no real solutions ⓑ 1 1 ⓒ 2 2
ⓐ 1 1 ⓑ no real solutions no real solutions ⓒ 2 2
ⓐ factor factor ⓑ square root square root ⓒ Quadratic Formula Quadratic Formula
ⓐ Quadratic Formula Quadratic Formula ⓑ square root square root ⓒ factor factor
Section 9.4 Exercises
x = ± 3 , x = ± 2 x = ± 3 , x = ± 2
x = ± 15 , x = ± 2 i x = ± 15 , x = ± 2 i
x = ± 1 , x = ± 6 2 x = ± 1 , x = ± 6 2
x = ± 3 , x = ± 2 2 x = ± 3 , x = ± 2 2
x = −1 , x = 12 x = −1 , x = 12
x = − 5 3 , x = 0 x = − 5 3 , x = 0
x = 0 , x = ± 3 x = 0 , x = ± 3
x = ± 11 2 , x = ± 7 x = ± 11 2 , x = ± 7
x = 25 x = 25
x = 4 x = 4
x = 1 4 x = 1 4
x = 1 25 , x = 9 4 x = 1 25 , x = 9 4
x = −1 , x = −512 x = −1 , x = −512
x = 8 , x = −216 x = 8 , x = −216
x = 27 8 , x = − 64 27 x = 27 8 , x = − 64 27
x = 27 512 , x = 125 x = 27 512 , x = 125
x = 1 , x = 49 x = 1 , x = 49
x = −2 , x = − 3 5 x = −2 , x = − 3 5
x = −2 , x = 4 3 x = −2 , x = 4 3
Section 9.5 Exercises
Two consecutive odd numbers whose product is 255 are 15 and 17, and −15 and −17.
The first and second consecutive odd numbers are 24 and 26, and −26 and −24.
Two consecutive odd numbers whose product is 483 are 21 and 23, and −21 and −23.
The width of the triangle is 5 inches and the height is 18 inches.
The base is 24 feet and the height of the triangle is 10 feet.
The length of the driveway is 15.0 feet and the width is 3.3 feet.
The length of table is 8 feet and the width is 3 feet.
The length of the legs of the right triangle are 3.2 and 9.6 cm.
The length of the diagonal fencing is 7.3 yards.
The ladder will reach 24.5 feet on the side of the house.
The arrow will reach 400 feet on its way up in 2.8 seconds and on the way down in 11 seconds.
The bullet will take 70 seconds to hit the ground.
The speed of the wind was 49 mph.
The speed of the current was 4.3 mph.
The less experienced painter takes 6 hours and the experienced painter takes 3 hours to do the job alone.
Machine #1 takes 3.6 hours and Machine #2 takes 4.6 hours to do the job alone.
Section 9.6 Exercises
ⓐ down ⓑ up
ⓐ x = −4 x = −4 ; ⓑ ( −4 , −17 ) ( −4 , −17 )
ⓐ x = 1 x = 1 ; ⓑ ( 1 , 2 ) ( 1 , 2 )
y -intercept: ( 0 , 6 ) ; ( 0 , 6 ) ; x -intercept ( −1 , 0 ) , ( −6 , 0 ) ( −1 , 0 ) , ( −6 , 0 )
y -intercept: ( 0 , 12 ) ; ( 0 , 12 ) ; x -intercept ( −2 , 0 ) , ( −6 , 0 ) ( −2 , 0 ) , ( −6 , 0 )
y -intercept: ( 0 , −19 ) ; ( 0 , −19 ) ; x -intercept: none
y -intercept: ( 0 , 13 ) ; ( 0 , 13 ) ; x -intercept: none
y -intercept: ( 0 , −16 ) ; ( 0 , −16 ) ; x -intercept ( 5 2 , 0 ) ( 5 2 , 0 )
y -intercept: ( 0 , 9 ) ; ( 0 , 9 ) ; x -intercept ( −3 , 0 ) ( −3 , 0 )
The minimum value is − 9 8 − 9 8 when x = − 1 4 . x = − 1 4 .
The maximum value is 6 when x = 3.
The maximum value is 16 when x = 0.
In 5.3 sec the arrow will reach maximum height of 486 ft.
In 3.4 seconds the ball will reach its maximum height of 185.6 feet.
20 computers will give the maximum of $400 in receipts.
He will be able to sell 35 pairs of boots at the maximum revenue of $1,225.
The length of the side along the river of the corral is 120 feet and the maximum area is 7,200 square feet.
The maximum area of the patio is 800 feet.
Section 9.7 Exercises
ⓑ The graph of g ( x ) = x 2 + 4 g ( x ) = x 2 + 4 is the same as the graph of f ( x ) = x 2 f ( x ) = x 2 but shifted up 4 units. The graph of h ( x ) = x 2 − 4 h ( x ) = x 2 − 4 is the same as the graph of f ( x ) = x 2 f ( x ) = x 2 but shift down 4 units.
ⓑ The graph of g ( x ) = ( x − 3 ) 2 g ( x ) = ( x − 3 ) 2 is the same as the graph of f ( x ) = x 2 f ( x ) = x 2 but shifted right 3 units. The graph of h ( x ) = ( x + 3 ) 2 h ( x ) = ( x + 3 ) 2 is the same as the graph of f ( x ) = x 2 f ( x ) = x 2 but shifted left 3 units.
f ( x ) = −3 ( x + 2 ) 2 + 7 f ( x ) = −3 ( x + 2 ) 2 + 7
f ( x ) = 3 ( x + 1 ) 2 − 4 f ( x ) = 3 ( x + 1 ) 2 − 4
ⓐ f ( x ) = ( x + 3 ) 2 − 4 f ( x ) = ( x + 3 ) 2 − 4 ⓑ
ⓐ f ( x ) = ( x + 2 ) 2 − 1 f ( x ) = ( x + 2 ) 2 − 1 ⓑ
ⓐ f ( x ) = ( x − 3 ) 2 + 6 f ( x ) = ( x − 3 ) 2 + 6 ⓑ
ⓐ f ( x ) = − ( x − 4 ) 2 + 0 f ( x ) = − ( x − 4 ) 2 + 0 ⓑ
ⓐ f ( x ) = − ( x + 2 ) 2 + 6 f ( x ) = − ( x + 2 ) 2 + 6 ⓑ
ⓐ f ( x ) = 5 ( x − 1 ) 2 + 3 f ( x ) = 5 ( x − 1 ) 2 + 3 ⓑ
ⓐ f ( x ) = 2 ( x − 1 ) 2 − 1 f ( x ) = 2 ( x − 1 ) 2 − 1 ⓑ
ⓐ f ( x ) = −2 ( x − 2 ) 2 − 2 f ( x ) = −2 ( x − 2 ) 2 − 2 ⓑ
ⓐ f ( x ) = 2 ( x + 1 ) 2 + 4 f ( x ) = 2 ( x + 1 ) 2 + 4 ⓑ
ⓐ f ( x ) = − ( x − 1 ) 2 − 3 f ( x ) = − ( x − 1 ) 2 − 3 ⓑ
f ( x ) = ( x + 1 ) 2 − 5 f ( x ) = ( x + 1 ) 2 − 5
f ( x ) = 2 ( x − 1 ) 2 − 3 f ( x ) = 2 ( x − 1 ) 2 − 3
Section 9.8 Exercises
ⓑ ( − ∞ , −5 ) ∪ ( −1 , ∞ ) ( − ∞ , −5 ) ∪ ( −1 , ∞ )
ⓑ [ −3 , −1 ] [ −3 , −1 ]
ⓑ ( − ∞ , −6 ] ∪ [ 3 , ∞ ) ( − ∞ , −6 ] ∪ [ 3 , ∞ )
ⓑ [ −3 , 4 ] [ −3 , 4 ]
( − ∞ , −4 ] ∪ [ 1 , ∞ ) ( − ∞ , −4 ] ∪ [ 1 , ∞ )
( 2 , 5 ) ( 2 , 5 )
( − ∞ , −5 ) ∪ ( −3 , ∞ ) ( − ∞ , −5 ) ∪ ( −3 , ∞ )
[ 2 − 2 , 2 + 2 ] [ 2 − 2 , 2 + 2 ]
( − ∞ , 5 − 6 ) ∪ ( 5 + 6 , ∞ ) ( − ∞ , 5 − 6 ) ∪ ( 5 + 6 , ∞ )
( − ∞ , − 5 2 ] ∪ [ − 2 3 , ∞ ) ( − ∞ , − 5 2 ] ∪ [ − 2 3 , ∞ )
[ − 1 2 , 4 ] [ − 1 2 , 4 ]
( − ∞ , ∞ ) . ( − ∞ , ∞ ) .
no solution
y = ± 12 y = ± 12
a = ± 5 a = ± 5
r = ± 4 2 i r = ± 4 2 i
w = ± 5 3 w = ± 5 3
p = −1 , 9 p = −1 , 9
x = 1 4 ± 3 4 x = 1 4 ± 3 4
n = 4 ± 10 2 n = 4 ± 10 2
n = −5 ± 2 3 n = −5 ± 2 3
( x + 11 ) 2 ( x + 11 ) 2
( a − 3 2 ) 2 ( a − 3 2 ) 2
d = −13 , −1 d = −13 , −1
m = −3 ± 10 i m = −3 ± 10 i
v = 7 ± 3 2 v = 7 ± 3 2
m = −9 , −1 m = −9 , −1
a = 3 2 ± 41 2 a = 3 2 ± 41 2
u = −6 ± 2 2 u = −6 ± 2 2
p = 0 , 6 p = 0 , 6
y = − 1 2 , 2 y = − 1 2 , 2
c = − 1 3 ± 2 7 3 c = − 1 3 ± 2 7 3
x = 3 2 ± 1 2 i x = 3 2 ± 1 2 i
x = 1 4 , 1 x = 1 4 , 1
r = −6 , 7 r = −6 , 7
v = −1 ± 21 8 v = −1 ± 21 8
m = −4 ± 10 3 m = −4 ± 10 3
a = 5 12 ± 23 12 i a = 5 12 ± 23 12 i
u = 5 ± 21 u = 5 ± 21
p = 4 ± 5 5 p = 4 ± 5 5
c = − 1 2 c = − 1 2
ⓐ 1 ⓑ 2 ⓒ 2 ⓓ 2
ⓐ factor ⓑ Quadratic Formula ⓒ square root
x = ± 2 , x = ± 2 3 x = ± 2 , x = ± 2 3
x = ± 1 , x = ± 1 2 x = ± 1 , x = ± 1 2
x = 16 x = 16
x = 64 , x = 216 x = 64 , x = 216
Two consecutive even numbers whose product is 624 are 24 and 26, and −24 and −26.
The height is 14 inches and the width is 10 inches.
The length of the diagonal is 3.6 feet.
The width of the serving table is 4.7 feet and the length is 16.1 feet.
The speed of the wind was 30 mph.
One man takes 3 hours and the other man 6 hours to finish the repair alone.
ⓐ up ⓑ down
x = 2 ; ( 2 , −7 ) x = 2 ; ( 2 , −7 )
y : ( 0 , 15 ) x : ( 3 , 0 ) , ( 5 , 0 ) y : ( 0 , 15 ) x : ( 3 , 0 ) , ( 5 , 0 )
y : ( 0 , −46 ) x : none y : ( 0 , −46 ) x : none
y : ( 0 , −64 ) x : ( −8 , 0 ) y : ( 0 , −64 ) x : ( −8 , 0 )
The maximum value is 2 when x = 2.
The length adjacent to the building is 90 feet giving a maximum area of 4,050 square feet.
f ( x ) = 2 ( x − 1 ) 2 − 6 f ( x ) = 2 ( x − 1 ) 2 − 6
ⓐ f ( x ) = 3 ( x − 1 ) 2 − 4 f ( x ) = 3 ( x − 1 ) 2 − 4 ⓑ
ⓐ f ( x ) = −3 ( x + 2 ) 2 + 7 f ( x ) = −3 ( x + 2 ) 2 + 7 ⓑ
ⓑ ( − ∞ , −2 ) ∪ ( 3 , ∞ ) ( − ∞ , −2 ) ∪ ( 3 , ∞ )
[ −2 , 1 ] [ −2 , 1 ]
( 2 , 4 ) ( 2 , 4 )
[ 3 − 5 , 3 + 5 ] [ 3 − 5 , 3 + 5 ]
w = −2 , w = −8 w = −2 , w = −8
m = 1 , m = 3 2 m = 1 , m = 3 2
y = 2 3 y = 2 3
y = 1 , y = −27 y = 1 , y = −27
ⓐ down ⓑ x = −4 x = −4 ⓒ ( −4 , 0 ) ( −4 , 0 ) ⓓ y : ( 0 , 16 ) ; x : ( −4 , 0 ) y : ( 0 , 16 ) ; x : ( −4 , 0 ) ⓔ minimum value of −4 −4 when x = 0 x = 0
( − ∞ , − 5 2 ) ∪ ( 2 , ∞ ) ( − ∞ , − 5 2 ) ∪ ( 2 , ∞ )
The diagonal is 3.8 units long.
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- Authors: Lynn Marecek
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- Book title: Intermediate Algebra
- Publication date: Mar 14, 2017
- Location: Houston, Texas
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- Section URL: https://openstax.org/books/intermediate-algebra/pages/chapter-9
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Quadratic Equations Practice Test Questions And Answers
Take our " Quadratic Equations Practice Test Questions and Answers " to check your knowledge on this topic. Quadratic equations are an important topic in mathematics. All the students need to learn and should have a good command of this important topic. In this quiz, you just have to pick the correct option from the other option choices given below to get a great score. Additionally, this quiz is also good if you want to prepare for your quadratic test. We are sure that you Have fun learning Maths!
-1x 2 + 0x + 49 = 0
X = -9 and -6
X = 7 and -7
X = 8 and 3
X = 7 and -3
X = 9 and -9
Rate this question:
-1x 2 + 2x + 48 = 0
X = -2 and 1
X = -1 and -7
X = 8 and -8
X = 8 and -6
1x 2 + 5x - 14 = 0
X = -1 and 2
X = -7 and 2
1x 2 + 10x + 21 = 0
X = -7 and -3
X = -7 and 3
X = 8 and 6
X = 10 and 11
-1x 2 + 3x + 28 = 0
X = -6 and -8
X = 9 and 4
X = 6 and -5
X = -7 and -4
X = 7 and 4
What is the vertex of the following equation: x 2 - 8x + 15 = 0?
What is the axis of symmetry and range of the following function: x 2 - 8x + 15 = 0.
Axis: x=4 ; Range: (-1,infinity)
Axis: x=-4 ; Range: (-1, infinity)
Axis: x=-1 ; Range: (4, infinity)
Axis: x=-1 ; Range: (-4, infinity)
What is the vertex of the following equation: -x 2 - 9x - 8 = 0?
(-4.5, 12.25)
What is the range of the following function: -x 2 + 2x + 8 = 0?
(infinity, 9)
(-infinity, infinity)
(9, infinity)
(-9, infinity)
(-infinity, 9)
What is the domain of the following function: -x 2 + 2x + 8 = 0?
(-infinity,infinity)
(infinity,9)
(1, infinity)
(9,infinity)
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4th - 5th
Discriminant, 9th - 10th , extrema and concavity, 11th - 12th , inequality key words.
Algebra 1 Quadratic Test
Mathematics.
30 questions
- 1. Multiple Choice 2 minutes 1 pt Determine the values of a, b, and c for the quadratic equation: 4x 2 – 8x = 3 a = 4, b = -8, c = 3 a = 4, b =-8, c =-3 a = 4, b = 8, c = 3 a = 4, b = 8, c = -3
- 2. Multiple Choice 1.5 minutes 1 pt Use the quadratic formula to solve 2x 2 + 2x - 12? -2, 3 2, 3 2, -3 -2, -3
- 3. Multiple Choice 1 minute 1 pt Identify the 'b' value: y = 16x 2 -8x -24 16 -8 8 -24
- 4. Multiple Choice 1 minute 1 pt The quadratic equation can be used to solve quadratic equations that cannot be factored. True False
- 5. Multiple Choice 30 seconds 1 pt What should you do first in solving this equation? x 2 + 6x - 13 = 3 Get factored form Write down: a=1, b=6, c=-13 Make it equal 0 by subtracting 3 on each side Type it all in a calculator.
What is the vertex of this quadratic equation?
y = -2(x + 2) 2 + 4
y = 2(x - 2) 2 + 4
- 11. Multiple Choice 1.5 minutes 1 pt What do we call the graph of a quadratic function? parabola linear cubic sinusoidal
- 12. Multiple Choice 30 seconds 1 pt What is the maximum/minimum of a parabola called? vertex point top bottom
- 13. Multiple Choice 1 minute 1 pt The axis of symmetry is a line that goes through the... y-intercept any random point vertex x-axis or y-axis
Which best describes the vertex of a parabola?
Any point on the parabola.
A point on the x-axis.
The point where the curve changes direction.
A point on the y-axis.
- 15. Multiple Choice 1 minute 1 pt A parabola has a vertex at (-3,2). Where is the axis of symmetry? y = -2 x = 3 x = -3 y = 2
Factor x 2 + 7x + 6
(x - 6)(x - 1)
(x + 3)(x + 2)
(x + 6)(x + 1)
(x - 3)(x - 2)
Factor x 2 - 4x - 12
(x - 6)(x + 3)
(x + 4)(x - 3)
(x - 6)(x + 2)
(x + 6)(x - 2)
What are coordinates of the vertex of a parabola often represented by?
(x 2 , y 2 )
(r 2 , d 2 )
A parabola has a vertex at (1,6) and passes through (3,-18). Solve for "a" and use it to write the equation in vertex form.
Formula: f(x) = a(x - h) 2 + k
f(x) = 3(x - 1) 2 - 18
f(x) = -6(x - 1) 2 + 6
f(x) = 6(x - 3) 2 - 18
f(x) = -3(x + 1) 2 - 6
Convert the equation from vertex form to standard form:
y = -3(x + 5) 2 - 4
y = 9x 2 - 15x + 21
y = -3x 2 - 75x - 4
y = 9x 2 + 90x + 221
y = -3x 2 - 30x - 79
Convert the equation into standard form:
y = -5(x + 2) 2 - 10
y = -5x 2 - 20x - 30
y = -5x 2 - 4x - 10
y = 25x 2 + 100x + 90
y = 25x 2 - 10x - 30
- 22. Multiple Choice 30 seconds 1 pt Convert f(x) = -4(x - 1) 2 +7 to standard form. f(x) = -4x 2 + 3 f(x) = -4x 2 - 8x + 17 f(x) = -4x 2 +8x - 11 f(x) = -4x 2 +8x + 3
- 23. Multiple Choice 5 minutes 1 pt Convert y = 3(x+1) 2 - 8 into standard form. y=3x 2 + 6x - 5 y=3x 2 - 6x - 5 y=3x 2 + 6x + 5 y=3x 2 - 6x + 5
- 24. Multiple Choice 5 minutes 1 pt What is the vertex form for a vertex of (1, 5) and when a=3? y = 3(x-1) 2 +5 y = 1(x-3) 2 +5 y = 3(x-5) 2 +1 y = 3(x+1) 2 +5
- 25. Multiple Choice 5 minutes 1 pt Which of the following equations matches standard form of a quadratic? ax + by = c y = a(x - h) 2 + k y = ax 2 + bx + c y = mx + b
- 26. Multiple Choice 5 minutes 1 pt If a = 3 and the vertex is (4, 2) what is the equation for the graph of the parabola? y = 3(x - 4) 2 - 2 y = 3(x+4) 2 + 2 y = 3(x - 4) 2 + 2 y = 3(x + 4) 2 - 2
If given the equation y = 3(x + 5) 2 - 4, what is the vertex of the parabola?
- 29. Multiple Choice 5 minutes 1 pt Solve using the quadratic formula. 2x 2 - 9x - 35 = 0 x = 7/2, x = -6 x = -5/2, x =5 x = -3/7, x =6 x = -5/2, x = 7
- 30. Multiple Choice 5 minutes 1 pt Solve 2x 2 + 7x - 15 = 0 -1.5 or 5 No Solution -5 or 1.5 0.7 or 5
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Unit 1: Algebra foundations
Unit 2: solving equations & inequalities, unit 3: working with units, unit 4: linear equations & graphs, unit 5: forms of linear equations, unit 6: systems of equations, unit 7: inequalities (systems & graphs), unit 8: functions, unit 9: sequences, unit 10: absolute value & piecewise functions, unit 11: exponents & radicals, unit 12: exponential growth & decay, unit 13: quadratics: multiplying & factoring, unit 14: quadratic functions & equations, unit 15: irrational numbers, unit 16: creativity in algebra.
IMAGES
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COMMENTS
Solve each equation with the quadratic formula. - Calculate your answer as a decimal rounded to the nearest thousandth. ... Answers to Solving Quadratics - TEST REVIEW (ID: 1) 1) {-4, 3} 2) {-4, 4} 3) {6, 2} 4) {-6, 0 ... 5 + 105 8, 5 - 105 8} 18) {-4 + 219 5, -4 - 219 5} 19) {2 + 26 5, 2 - 26 5} 20) {3 + 317 8, 3 - 317 8} Title: Infinite ...
Familiar Attempted Not started Quiz Unit test About this unit We've seen linear and exponential functions, and now we're ready for quadratic functions. We'll explore how these functions and the parabolas they produce can be used to solve real-world problems. Intro to parabolas Learn Parabolas intro Interpreting a parabola in context
Review: Finding the GCF of Two Numbers Common Factors • Factors that are shared by two or more numbers Greatest Common Factor (GCF) • To find the GCF create a factor t-chart for each number and find the largest common factor Example: Find the GCF of 56 and 104 Practice: Find the GCF of the following numbers. a. 30, 45 b. 12, 54
The graphs of y= (x-c)² is a --- translation of the parent function y=x². horizontal. the quadratic formula is: x=-b±√b²-4ac÷2a. the discriminant (radican of the formula) Study with Quizlet and memorize flashcards containing terms like fat like a --- narrow like a ---, when a in y=ax² is positive, the parabola opens ---., when a in y ...
16 Quiz Review Quadratic Equations REVIEW FOR QUIZ! NAME: __________________________ DUE TUES/WED Solve each equation (use the method provided) Solve each equation. SOLVING: WHICH METHOD SHOULD YOU USE? Explain why! Solve: Choose which method is best =) Find the discriminant and determine the number and type of solutions.
3. Solve the function graphically. y = x2 - 4x - 5 4. Solve the function graphically. y = 2 (x + 1) (x - 3) Vertex: _______ Solutions: ________ Vertex: _______ Solutions: ________ Section 1: Factoring Factor Completely! Section 2: Graph the Quadratic Equations 3. y = -2x2 + 8 Vertex: _________________ x - Intercepts: ____________
Find step-by-step solutions and answers to enVision Algebra 1 - 9780328931576, as well as thousands of textbooks so you can move forward with confidence. ... Topic Review. Page 143: Explore and Reason. Page 143: Try It! Page 147: Practice and Problem Solving. ... Section 9-1: Solving Quadratic Equations Using Graphs and Tables. Section 9-2 ...
Algebra (all content) 20 units · 412 skills. Unit 1 Introduction to algebra. Unit 2 Solving basic equations & inequalities (one variable, linear) Unit 3 Linear equations, functions, & graphs. Unit 4 Sequences. Unit 5 System of equations. Unit 6 Two-variable inequalities. Unit 7 Functions. Unit 8 Absolute value equations, functions, & inequalities.
Unit test. Learn for free about math, art, computer programming, economics, physics, chemistry, biology, medicine, finance, history, and more. Khan Academy is a nonprofit with the mission of providing a free, world-class education for anyone, anywhere.
Algebra 1 - Mr. Allen-Black & Mrs. Gulamali Factoring & Solving Quadratics - TEST REVIEW Name_____ ID: 1 Date_____ Period____ ©\ G2P0E1A9R MKLuftnaX QSxoQf`t`wvatrYee mLcL]CB.H N `ARluld MrNiGglhstusI MruehstexryvQeYd^.-1-Factor each completely. 1) 7b2 + 5b 2) 9a2 - 12a + 4 3) -18x6 + 6x5 + 14x4 + 12x34) 4n2 - 25
SOLVING QUADRATIC EQUATIONS USING THE QUADRATIC FORMULA 2 + + = 0 = − ± √ − Steps: Get all terms on one side and set equal to 0 Plug in the a, b and c into the equation
How do we find slope? What are the forms of linear equations? The review articles below explore all topics related to linear equations including slope, forms of equations, and graphing linear equations. We provide detailed step-by-step directions, practice problems, and helpful video summaries. How to Teach Linear Equations Review topic
Skill plans. IXL plans. Washington state standards. Textbooks. Test prep. Awards. Improve your math knowledge with free questions in "Solve a quadratic equation using the quadratic formula" and thousands of other math skills.
zero product property. M · N = 0 if and only if M = 0 or N = 0 (or both) The following steps can be used to solve a quadratic equation by the factoring method. 1. Write the quadratic equation in general form (ax2 + bx + c = 0). 2. Find the factors of ax2 + bx + c. 3. Apply the zero product property.
This article reviews how to apply the formula. What is the quadratic formula? The quadratic formula says that x = − b ± b 2 − 4 a c 2 a for any quadratic equation like: a x 2 + b x + c = 0 Example We're given an equation and asked to solve for q : 0 = − 7 q 2 + 2 q + 9
Here is a set of practice problems to accompany the Quadratic Equations - Part I section of the Solving Equations and Inequalities chapter of the notes for Paul Dawkins Algebra course at Lamar University.
Introduction; 9.1 Solve Quadratic Equations Using the Square Root Property; 9.2 Solve Quadratic Equations by Completing the Square; 9.3 Solve Quadratic Equations Using the Quadratic Formula; 9.4 Solve Quadratic Equations in Quadratic Form; 9.5 Solve Applications of Quadratic Equations; 9.6 Graph Quadratic Functions Using Properties; 9.7 Graph Quadratic Functions Using Transformations
Properties Notes Properties (1.4) Worksheet Key Distributive Property and Order of Operations Notes Combining Like Terms and Distributive Property Worksheet Key Unit 1 Review Unit 1 Review Key Solving Equations Solving One-Step Equations Notes One-Step Equations Worksheet Key Solving Two-Step Equations Notes Two-Step Equations Worksheet Key
Quadratic equations create 2 solutions. Sometimes they are the same solution and the equation degrades to a single solution. By dividing by "p", you destroy / lose the 2nd solution. You can't know that the 2nd solution will be a complex number at this point in solving the equation. And, as you get into higher level math, there are applications ...
Correct Answer B. X = 7 and -7 Explanation The given equation is a quadratic equation of the form ax^2 + bx + c = 0. By factoring or using the quadratic formula, we can find the values of x that satisfy the equation.
Algebra 1 Quadratic Test quiz for 9th grade students. Find other quizzes for Mathematics and more on Quizizz for free! ... The quadratic equation can be used to solve quadratic equations that cannot be factored. True. False. 5. Multiple Choice. 30 seconds. ... Answer choices . Tags . Log in. 10 Qs . Symmetry 7.5K plays 4th - 5th 10 Qs ...
0 likes, 1 comments - absolutevaluemath on December 10, 2023: "Get your hands on an Algebra 1 or Algebra 2 pack of 5 Digital Matching Activities! This is the UL..." High School Math on Instagram: "Get your hands on an Algebra 1 or Algebra 2 pack of 5 Digital Matching Activities!
The Algebra 1 course, often taught in the 9th grade, covers Linear equations, inequalities, functions, and graphs; Systems of equations and inequalities; Extension of the concept of a function; Exponential models; and Quadratic equations, functions, and graphs. Khan Academy's Algebra 1 course is built to deliver a comprehensive, illuminating, engaging, and Common Core aligned experience!