Free Printable Algebra II Term Benchmark Study Guide

1.

What is the DOMAIN of the graph?

a)

$\left[-7,5\right)$

b)

$\left[-3,\ 1\right]$

c)

$\left[-3,\ 1\right)$

d)

$\left[-7,\ 5\right]$

2.

What is the DOMAIN of the graph?

a)

$\left[-7,5\right)$

b)

$\left[-3,\ 1\right]$

c)

$\left[-3,\ 1\right)$

d)

$\left[-7,\ 5\right]$

3.

What is the RANGE of the graph?

a)

$\left(-7,5\right)$

b)

$\left[-7,5\right)$

c)

$\left[-3,\ 1\right)$

d)

$\left(-3,1\right)$

4.

What is the DOMAIN?

a)

$\left[-3,\ 2\right)$

b)

$\left[-7,\ 2\right)$

c)

$\left(-3,\ 2\right)$

d)

$\left(-7,\ 2\right)$

5.

What is the RANGE?

a)

$\left(-7,\ 2\right)$

b)

$\left[-7,\ 2\right]$

c)

$\left[-3,\ 2\right)$

d)

$\left(-3,\ 2\right)$

6.

What is the DOMAIN?

a)

$\left(-\infty,\ \infty\right)$

b)

$\left(-\infty,\ 6\right]$

c)

$\left[-10,\ \infty\right)$

d)

$\left[-10,\ 10\right]$

7.

What is the RANGE?

a)

$\left(-\infty,\ 6\right]$

b)

$\left[-10,\ 6\right]$

c)

$\left[-10,\ \infty\right)$

d)

$\left(-\infty,\ \infty\right)$

8.

What is the DOMAIN of this linear function?

a)

$\left[-6,\ 6\right]$

b)

$\left[0,\ 6\right]$

c)

$\left(-\infty,\ \infty\right)$

d)

No Solution

9.

What is the RANGE of this linear function?

a)

$\left(-\infty,\ \infty\right)$

b)

$\left[0,\ 6\right]$

c)

$\left[-6,\ 6\right]$

d)

No Solution

10.

What is the DOMAIN?

a)

$-3\le x<2$

b)

$-\infty<x<\infty$

c)

$-7\le x\le2$

d)

$-\infty<x\le2$

11.

What is the RANGE?

a)

$-3\le y<2$

b)

$-\infty<y<\infty$

c)

$-7\le y\le2$

d)

$-\infty<y\le2$

12.

What is the DOMAIN of the graph?

a)

$-3\le x\le3$

b)

$-\infty<x<\infty$

c)

$-2\le x\le10$

d)

$-3\le x<\infty$

13.

What is the RANGE of the graph?

a)

$-3\le y\le3$

b)

$-\infty<y<\infty$

c)

$-2\le y\le10$

d)

$-3\le y<\infty$

14.

What is the RANGE of the function?

a)

$-\infty<y<\infty$

b)

$1<y<3$

c)

$-\infty<y<3$

d)

$2<y<\infty$

15.

Identify the graph with a x-intercept of 3 and a y-intercept of - 1

a)

b)

c)

d)

16.

Identify the graph with a x-intercept of -2 and y-intercept of 2

a)

b)

c)

d)

17.

What is the x-intercept?

a)

12

b)

-3

c)

8

d)

0

18.

What is the y-intercept?

a)

12

b)

-3

c)

8

d)

0

19.

What are the x- intercepts?

a)

x= 0 and x= -4

b)

x= 0 and x= 4

c)

y= 0

d)

x= 2

20.

Find the x and y intercepts
4x - 5y = 40

a)

x intercept is 10
y intercept is 8

b)

x intercept is 10
y intercept is 20

c)

x intercept is 8
y intercept is 10

d)

x intercept is 10
y intercept is -8

21.

What is the maximum value (y-value only)?

a)

5

b)

0

c)

-5

d)

2

22.

What is the minimum value (y-value only)?

a)

-1

b)

0

c)

-5

d)

-3

23.

Grace is tracking the temperature over a week. What is the minimum temperature recorded (y-value only)?

a)

-5

b)

-3

c)

0

d)

-1

24.

How many extrema are there in this graph?

a)

2 max, 2 min

b)

3 max, 2 min

c)

2 max, 3 min

25.

What are the local maxima of this graph?

a)

local maximum at (2.2, 3.9)

b)

local maximum at (-8, 5)

c)

local maximum at (5, -8)⋃(3.9, 2.2)

d)

local maximum at (-8, 5)⋃(2.2, 3.9)

26.

What is the absolute max?

a)

(0, 36)

b)

(−2.55, −6.55), (2.55, −6.55)

c)

(−∞, ∞)

d)

None

27.

Where is the function decreasing?

a)

(-∞, -1)

b)

(-1, ∞)

c)

(-∞, 3)

d)

(-∞, ∞)

28.

Determine end behavior of function with the given graph

a)

$x\rightarrow-\infty;\ f\left(x\right)\ \rightarrow\ -\infty$ $x\rightarrow+\infty;\ f\left(x\right)\rightarrow+\infty$

b)

$x\rightarrow-\infty;\ f\left(x\right)\rightarrow+\infty$ $x\rightarrow+\infty;\ f\left(x\right)\rightarrow-\infty$

c)

$x\rightarrow-\infty;\ f\left(x\right)\rightarrow-\infty$ $x\rightarrow+\infty;\ f\left(x\right)\rightarrow\ -\infty$

d)

$x\rightarrow-\infty;\ f\left(x\right)\rightarrow+\infty$ $x\rightarrow+\infty;\ f\left(x\right)\rightarrow+\infty$

29.

Determine end behavior of function with the given graph

a)

$x\rightarrow-\infty;\ f\left(x\right)\ \rightarrow\ -\infty$ $x\rightarrow+\infty;\ f\left(x\right)\rightarrow+\infty$

b)

$x\rightarrow-\infty;\ f\left(x\right)\rightarrow+\infty$ $x\rightarrow+\infty;\ f\left(x\right)\rightarrow-\infty$

c)

$x\rightarrow-\infty;\ f\left(x\right)\rightarrow-\infty$ $x\rightarrow+\infty;\ f\left(x\right)\rightarrow\ -\infty$

d)

$x\rightarrow-\infty;\ f\left(x\right)\rightarrow+\infty$ $x\rightarrow+\infty;\ f\left(x\right)\rightarrow+\infty$

30.

Determine end behavior of function with the given graph

a)

$x\rightarrow-\infty;\ f\left(x\right)\ \rightarrow\ -\infty$ $x\rightarrow+\infty;\ f\left(x\right)\rightarrow+\infty$

b)

$x\rightarrow-\infty;\ f\left(x\right)\rightarrow+\infty$ $x\rightarrow+\infty;\ f\left(x\right)\rightarrow-\infty$

c)

$x\rightarrow-\infty;\ f\left(x\right)\rightarrow-\infty$ $x\rightarrow+\infty;\ f\left(x\right)\rightarrow\ -\infty$

d)

$x\rightarrow-\infty;\ f\left(x\right)\rightarrow+\infty$ $x\rightarrow+\infty;\ f\left(x\right)\rightarrow+\infty$

31.

Determine end behavior of function with the given graph

a)

$x\rightarrow-\infty;\ f\left(x\right)\ \rightarrow\ -\infty$ $x\rightarrow+\infty;\ f\left(x\right)\rightarrow+\infty$

b)

$x\rightarrow-\infty;\ f\left(x\right)\rightarrow+\infty$ $x\rightarrow+\infty;\ f\left(x\right)\rightarrow-\infty$

c)

$x\rightarrow-\infty;\ f\left(x\right)\rightarrow-\infty$ $x\rightarrow+\infty;\ f\left(x\right)\rightarrow\ -\infty$

d)

$x\rightarrow-\infty;\ f\left(x\right)\rightarrow+\infty$ $x\rightarrow+\infty;\ f\left(x\right)\rightarrow+\infty$

32.

Describe the end behavior of the graph.

a)

x → ∞, y→ ∞ and
x→ ∞, y→⁻∞

b)

x → ∞, y→ ∞ and
x→⁻∞, y→∞

c)

None of these

d)

x →∞,y→⁻∞ and
x→∞, y→⁻∞

33.

Describe the end behavior of the graph.

a)

x →∞, y→⁻∞ and x →⁻∞,y→⁻∞

b)

x →∞, y→∞ and x→⁻∞, y→∞

c)

x →∞, y→∞ and x→⁻∞, y→0

d)

x →∞,y→∞ and x→⁻∞, y→⁻∞

34.

What is the increasing interval on the function shown?

a)

$\left(-\infty,\ 1\right)$

b)

$\left(-\infty,\ 2\right)$

c)

$\left(2,\ \infty\right)$

d)

$\left(1,\ \infty\right)$

35.

When is the function decreasing?

a)

(30, 55)

b)

(40, 60]

c)

(15, 40)

d)

(60, -40)

36.

What is the decreasing interval on the function shown?

a)

$\left(-\infty,\ -3\right)$

b)

$\left(-\infty,\ -4\right)$

c)

$\left(-4,\ \infty\right)$

d)

$\left(-3,\ \infty\right)$

37.

Determine the interval in which this function is INCREASING.

a)

(-4, ∞)

b)

(-3, ∞)

c)

(∞, -3)

d)

(-∞, -4)

38.

Determine the interval in which this function is DECREASING.

a)

(-3, ∞)

b)

(-3, ∞)

c)

(-∞, -4)

d)

(-∞, -3)

39.

Where is this graph increasing or decreasing?

a)

Increasing: $\left(-7,\ -3\right)$

Decreasing: $\left(-7,\ 2\right)$

b)

Increasing: $\left(0,\ 2\right)$

Decreasing: $\left(-3,\ 0\right)$

c)

Increasing: $\left(-3,\ 0\right)$

Decreasing: $\left(0,\ 2\right)$

d)

Increasing: $\left(-7,\ 2\right)$

Decreasing: $\left(-7,\ -3\right)$

40.

Where is this graph increasing or decreasing?

a)

Increasing: $\left(-\infty,\ -2\right)$

Decreasing: $\left(-2,\ \infty\right)$

b)

Increasing: $\left(-2,\ \infty\right)$

Decreasing: $\left(-\infty,\ -2\right)$

c)

Increasing: $\left(-\infty,\ 6\right)$

Decreasing: $\left(6,\ \infty\right)$

d)

Increasing: $\left(-10,\ -2\right)$

Decreasing: $\left(-2,\ 6\right)$

41.

Where is this graph increasing or decreasing?

a)

Increasing: $\left(-6,\ -3\right),\ \left(0,\ 3\right)$

Decreasing: $\left(-3,\ 0\right),\ \left(3,\ 6\right)$

b)

Increasing: $\left(-3,\ 0\right),\ \left(3,\ 6\right)$

Decreasing: $\left(-6,\ -3\right),\ \left(0,\ 3\right)$

c)

Increasing: $\left(-2,\ 6\right),\ \left(0,\ 3\right)$

Decreasing: $\left(2,\ 4\right),\ \left(0,\ 3\right)$

d)

Increasing: $\left(2,\ 4\right),\ \left(0,\ 3\right)$

Decreasing: $\left(-2,\ 6\right),\ \left(0,\ 3\right)$

42.

What is the increasing interval(s) on the function shown?

a)

$-\infty<x<-15\ or\ 9<x<-15$

b)

$-2<x<9\ or\ 2<x<\infty$

c)

$-\infty<x<-2\ or\ 0<x<2$

d)

$-2<x<0\ or\ 2<x<\infty$

43.

What is the decreasing interval(s) on the function shown?

a)

$-\infty<x<-15\ \ or\ \ 9<x<-15$

b)

$-2<x<9\ or\ 2<x<\infty$

c)

$-\infty<x<-2\ or\ 0<x<2$

d)

$-2<x<0\ or\ 2<x<\infty$

44.

Label the transformations that a, b, c, & d represent in a function.

a)Vertical Stretch/Shrink

b)Vertical Shift

c)Horizontal Stretch/Shrink

d)Horizontal Shift

1

2

3

4

1)

2)

3)

4)

45.

What are the following transformations?

g(x) = - (x+2)

a)

reflection over the y axis and 2 units to the right

b)

reflection over the x axis and 2 units right

c)

reflection over the y axis and 2 units left

d)

reflection over the x axis and 2 units left

46.

If (2, 3) is on the graph of y = f(x), which of the following coordinates will be on the graph of y = f(x + 1) + 3

a)

(3 , 6)

b)

(1 , 6)

c)

(5 , 0)

d)

(-1 , 0)

47.

What are the following transformations:
g(x) = f(-x) - 4

a)

reflection over the x axis and 4 units right

b)

reflection over the x axis and 4 units down

c)

reflection over the y axis and 4 units right

d)

reflection over the y axis and 4 units down

48.

Which of the following transformations are present?
-2f(x - 1) + 2

a)

reflection over the y axis

b)

reflection over the x axis

c)

shift left 1

d)

shift down 1

49.

Given f(x) = (x-3)² + 5. What transformations took place from the original function f(x)?

a)

Left 3 and up 5

b)

Right 3 and down 5

c)

Left 3 and down 5

d)

Right 3 and up 5

50.

$-f\left(x+3\right)+4$

Describe the transformations:

a)

Shifted left 3 units
Shifted up 4 units

b)

Reflection over the y-axis
Shifted right 3 units
Shifted up 4 units

c)

Shifted right 3 units
Shifted up 4 units

d)

Reflection over the x-axis
Shifted left 3 units
Shifted up 4 units

51.

Describe the transformations

$g\left(x+4\right)-6$

a)

4 Units Left

6 Units Up

b)

4 Units Left

6 Units Down

c)

4 Units Right

6 Units Up

d)

4 Units Right

6 Units Down

52.

If g(x) is formed by transforming f(x), how would we stretch f(x) vertically by a factor of 3?
$f(x)=3\left(5x-4\right)+2$

a)

Multiply 3 by 3

b)

Divide 3 by 3

c)

Multiply 5 by 3

d)

Divide 5 by 3

53.

If g(x) is formed by transforming f(x), how would we find $g(x)=3\left(x\right)$ ?
$f(x)=3\left(5x-4\right)+2$

a)

Multiply 3 by 3

b)

Divide 3 by 3

c)

Multiply 5 by 3

d)

Divide 5 by 3

54.

If g(x) is formed by transforming f(x), how would we stretch f(x) horizontally by a factor of 3?
$f(x)=3\left(5x-4\right)+2$

a)

Multiply 3 by 3

b)

Divide 3 by 3

c)

Multiply 5 by 3

d)

Divide 5 by 3

55.

If g(x) is formed by transforming f(x), how would we find $g(x)=\left(\frac{1}{3}x\right)$ ?
$f(x)=3\left(5x-4\right)+2$

a)

Multiply 3 by 3

b)

Divide 3 by 3

c)

Multiply 5 by 3

d)

Divide 5 by 3

56.

If g(x) is formed by transforming f(x), how would we shrink f(x) horizontally by a factor of 3?
$f(x)=3\left(5x-4\right)+2$

a)

Multiply 3 by 3

b)

Divide 3 by 3

c)

Multiply 5 by 3

d)

Divide 5 by 3

57.

If g(x) is formed by transforming f(x), how would we find $g(x)=\left(3x\right)$ ?
$f(x)=3\left(5x-4\right)+2$

a)

Multiply 3 by 3

b)

Divide 3 by 3

c)

Multiply 5 by 3

d)

Divide 5 by 3

58.

If g(x) is formed by transforming f(x), how would we shrink f(x) vertically by a factor of 3?
$f(x)=3\left(5x-4\right)+2$

a)

Multiply 3 by 3

b)

Divide 3 by 3

c)

Multiply 5 by 3

d)

Divide 5 by 3

59.

If g(x) is formed by transforming f(x), how would we find $g(x)=\frac{1}{3}x$ ?
$f(x)=3\left(5x-4\right)+2$

a)

Multiply 3 by 3

b)

Divide 3 by 3

c)

Multiply 5 by 3

d)

Divide 5 by 3

60.

If g(x) is formed by transforming f(x), how would we shift f(x) up by 3 units?
$f(x)=3\left(5x-4\right)+2$

a)

Add 3 to 2

b)

Subtract 3 from 2

c)

Subtract 3 from -4

d)

Add 3 to -4

61.

If g(x) is formed by transforming f(x), how would we find $g(x)=x+3$ ?
$f(x)=3\left(5x-4\right)+2$

a)

Add 3 to 2

b)

Subtract 3 from 2

c)

Subtract 3 from -4

d)

Add 3 to -4

62.

If g(x) is formed by transforming f(x), how would we shift f(x) down by 3 units?
$f(x)=3\left(5x-4\right)+2$

a)

Add 3 to 2

b)

Subtract 3 from 2

c)

Subtract 3 from -4

d)

Add 3 to -4

63.

If g(x) is formed by transforming f(x), how would we find $g(x)=x-3$ ?
$f(x)=3\left(5x-4\right)+2$

a)

Add 3 to 2

b)

Subtract 3 from 2

c)

Subtract 3 from -4

d)

Add 3 to -4

64.

If g(x) is formed by transforming f(x), how would we shift f(x) left by 3 units?
$f(x)=3\left(5x-4\right)+2$

a)

Add 3 to 2

b)

Subtract 3 from 2

c)

Subtract 3 from -4

d)

Add 3 to -4

65.

If g(x) is formed by transforming f(x), how would we find $g(x)=\left(x+3\right)$ ?
$f(x)=3\left(5x-4\right)+2$

a)

Add 3 to 2

b)

Subtract 3 from 2

c)

Subtract 3 from -4

d)

Add 3 to -4

66.

If g(x) is formed by transforming f(x), how would we shift f(x) right by 3 units?
$f(x)=3\left(5x-4\right)+2$

a)

Add 3 to 2

b)

Subtract 3 from 2

c)

Subtract 3 from -4

d)

Add 3 to -4

67.

If g(x) is formed by transforming f(x), how would we find $g(x)=\left(x-3\right)$ ?
$f(x)=3\left(5x-4\right)+2$

a)

Add 3 to 2

b)

Subtract 3 from 2

c)

Subtract 3 from -4

d)

Add 3 to -4

68.

Describe the transformations that maps
y = g(x) to y = - g(x + 6) - 10

a)

Reflect over y-axis
Shifted down 10 units
Shifted left 6 units

b)

Reflect over x-axis
Shifted up 10 units
Shifted left 6 units

c)

Reflect over y-axis
Shifted up 10 units
Shifted right 6 units

d)

Reflect over x-axis
Shifted down 10 units
Shifted left 6 units

69.

In the graph of the function y=x², which equation moves the graph down 5 units?

a)

y = x² - 5

b)

y = x² + 5

c)

y = (x - 5)²

d)

y = (x + 5)²

70.

y=(x+2)²+4

*Mark all that apply.

a)

reflection across x-axis

b)

left 2

c)

up 4

d)

right 2

71.

Select all the equations that show a vertical shift from its parent function.

a)

$y=\left|x+1\right|$

b)

$y=x^3+4$

c)

$y=x-10$

d)

$y=\left(x-3\right)^2$

e)

$y=x^2-1$

72.

Select all equations that show a horizontal shift from its parent function.

a)

$y=\left|x-4\right|$

b)

$y=\left(x-9\right)^3$

c)

$y=x^2+8$

d)

$y=\left|x\right|-5$

e)

$y=\sqrt{x}+1$

73.

Describe the transformations:

y = x² to y = 2(x+3)² - 5?

a)

Horizontal Stretch by 2, shift 3 units left and 5 down

b)

Horizontal Stretch by 2, shift 5 units left and 3 up

c)

Vertical Stretch by 2, shift 3 units left and 5 down

d)

Vertical Shrink by 1/2, shift 5 units left and 3 up

74.

Choose the equation that best matches the graphed function.

a)

$f(x)=|x-4|+3$

b)

$f(x)=|x-3|+4$

c)

$f(x)=|x-4|-3$

d)

$f(x)=|x+4|+3$

75.

Use the graphs of f and g to describe the transformation from the graph of f to the graph of g.

a)

The graph of g is a vertical translation 4 units up from the graph f

b)

The graph of g is a horizontal translation of the graph of f, 4 units right

c)

The graph of g is a horizontal translation of the graph of f, 4 units left

d)

The graph of g is a vertical stretch of the graph of f, by a factor of 7

76.

f(x) is shown. If $g\left(x\right)=-4\cdot f\left(x\right)-2$ which of the following graphs shows g(x)?

a)

b)

c)

d)

77.

Is the graph an even, odd, or neither function?

a)

Even

b)

Odd

c)

Neither

78.

Even, odd, or neither?

a)

Even

b)

Odd

c)

Neither

79.

Is the table even, odd or neither?

a)

Even

b)

Odd

c)

Neither

80.

Is the table even, odd or neither?

a)

Even

b)

Odd

c)

Neither

81.

Is the table even, odd or neither?

a)

Even

b)

Odd

c)

Neither

82.

What are the solutions to
v² + 6v + 5 = 0

a)

(1,0) and (0,0)

b)

(5, 0) and (-7, 0)

c)

(-5, 0) and (-1, 0)

d)

(6,0) and (0,0)

83.

Solve by factoring.
z² - 6z - 27 = 0

a)

z = 3 or z = 9

b)

z = 3 or z = -9

c)

z = -3 or z = 9

d)

z = -3 or z = -9

84.

Solve the following quadratic...

x² + 12x + 20 = 0

a)

x = 5, 4

b)

x = 2, 10

c)

x = -5, -4

d)

x = -2, -10

85.

What are the solutions to this equation? (x-3)(x+2)=0

a)

x=3,-2

b)

x=-3,2

c)

x=2,3

d)

x=3,2

86.

a)

±81

b)

±9

c)

±3

d)

No real solution

87.

Find the zeros of the following quadratic function.

$f\left(x\right)\ =\ x^2\ -\ x\ -30$

a)

{x = -5, 6}

b)

{x = -6, 5}

c)

{x = -3, 10}

d)

{x = -10, 3}

88.

Find the x-intercept(s) of the following quadratic.

$x^2\ -\ 12x\ =-\ 36$

a)

(6, 0)

b)

(6, 0) and (-6, 0)

c)

(-6, 0)

d)

no x-intercepts

89.

Solve for x.

5(x - 3)² + 1 = 81

a)

x = -1, 7

b)

x = -7, 1

c)

x = ± 9

d)

x = 3, 10

90.

Solve for x.

-7(x + 3)² + 63 = 0

a)

x = 0, 6

b)

x = -6, 12

c)

x = -6, 0

d)

x = 6, 12

91.

What are the factors AND solutions of x² + 2x – 3 = 0

a)

(x - 2)(x + 1); x=2, x=-1

b)

(x + 1)(x - 3); x=-1, x=3

c)

(x + 2)(x - 1); x=-2, x=1

d)

(x - 1)(x + 3); x=1, x=-3

92.

Solve
2x² + 17x + 21 = 0

a)

x= ^-21/₂, -17

b)

x= ²/₃, 16

c)

x=-7, ^-3/₂

d)

x=15, -³/₇

93.

What is this formula?

a)

This is the speed of light formula.

b)

This is the quadratic formula.

c)

This is the zero product property.

d)

This is scary.

94.

$x^2+5x\ +8\ =0$

Solve the given equation using the Quadratic Formula. Make sure you fully simplify your answer.

a)

$\frac{-5\pm\sqrt{57}}{2}$

b)

$\frac{5\pm\sqrt{57}}{2}$

c)

$\frac{-5\pm i\sqrt{7}}{2}$

d)

$\frac{5\pm i\sqrt{7}}{2}$

95.

$x^2-6x\ +12\ =0$

Solve the given equation using the Quadratic Formula. Make sure you fully simplify your answer.

a)

$3\pm i\sqrt{3}$

b)

$3\pm\ \sqrt{3}$

c)

$\frac{6\pm\sqrt{-12}}{2}$

d)

$3\pm i$

96.

$-x^2+6x\ -10\ =0$

Solve the given equation using the Quadratic Formula. Make sure you fully simplify your answer.

a)

$\frac{-6\pm\sqrt{76}}{-2}$

b)

$3\pm i$

c)

$-3\pm i$

d)

$\frac{6\pm\sqrt{76}}{-2}$

97.

$3x^2-3x\ +13\ =0$

Solve the given equation using the Quadratic Formula. Make sure you fully simplify your answer.

a)

$\frac{-3\pm7i\sqrt{3}}{6}$

b)

$\frac{3\pm7i\sqrt{3}}{6}$

c)

$\frac{-3\pm i\sqrt{163}}{6}$

d)

$\frac{3\pm i\sqrt{163}}{6}$

98.

What does the discriminant determine?

a)

Whether the graph goes up or down

b)

The vertex

c)

The number of Solutions

d)

The y-intercept

99.

What is the discriminant in the Quadratic Formula?

a)

-b + 4ac

b)

b - 4ac

c)

-b²- 4ac

d)

b²- 4ac

100.

If the discriminant is positive, how many real solutions does the graph have?

a)

2

b)

1

c)

0

101.

If the discriminant is negative, how many real solutions does the graph have?

a)

2

b)

1

c)

0

102.

If the discriminant is zero, how many real solutions does the graph have?

a)

2

b)

1

c)

0

103.

Find the discriminant: 2a² - 5a + 5 = 0

a)

44

b)

65

c)

-15

d)

-144

104.

How many real solutions does 2a² - 5a + 5 = 0 have?

a)

2

b)

1

c)

0

105.

What do you do to the b value to correctly complete the square?

a)

square it

b)

divide it by 2 and square the result

c)

divide it by 2 and take the square root of the result

d)

divide it by 2 only

106.

When do you use the plus or minus symbol?
±

a)

After taking the square root of both sides

b)

After adding the square to both sides

c)

After taking half of b

d)

After setting the equation equal to zero

107.

Complete the Square
x² + 6x = 5

a)

(x + 3)² = 5

b)

(x + 6)² = 9

c)

(x + 3)² = 14

d)

(x + 6)² = 14

108.

Solve by completing the square:
k² − 12k + 23 = 0

a)

{6 + √13, 6 - √13}

b)

{-6 + √13, -6 - √13}

c)

{6 + √59, 6 - √59}

d)

{-6 + √59, -6 - √59}

109.

Given: y = 2(x - 5) + 6, the vertex is

a)

(2,-5)

b)

(-5,6)

c)

(2,6)

d)

(5,6)

110.

Convert to vertex form.

a)

y=3(x+1)² - 8

b)

y=3(x-1)² - 8

c)

y=3(x+2)² - 8

d)

y=3(x-2)² - 8

111.

Convert to vertex form.

a)

y=-2(x+12)² - 67

b)

y=-2(x-12)² - 67

c)

y=-2(x-6)² - 67

d)

y=-2(x+6)² - 67

112.

When factoring $x^2-10x+25\ =\ 49$ what goes into the blank $\left(x-....\right)^2=49$

a)

5

b)

10

c)

7

d)

25

113.

Which equation shows vertex form of a quadratic function?

a)

$f\left(x\right)=a\left(x-h\right)^2+k$

b)

$f\left(x\right)=ax^2+bx+c$

c)

$f\left(x\right)=a\left(x-r_1\right)\left(x-r_2\right)$

d)

$x=-\frac{b}{2a}$

114.

What transformations have occurred in the function: $f\left(x\right)=-3\left(x-1\right)^2+6$

a)

Reflection across the x-axis; Vertical stretch of 3; Right 1; Up 6

b)

Horizontal compression of 3; Left 1; Down 6

c)

Horizontal stretch of 1; Reflection across the x-axis; Up 6

d)

Reflection across the x-axis; Vertical stretch of 3; Left 1; Up 6

115.

Which graph has factors of (x+1) and (x-3) ?

a)

b)

c)

d)

116.

Given the equation y = 3(x + 5)² - 4, what is the vertex of the parabola?

a)

(5, -4)

b)

(-5, -4)

c)

(-15, -4)

d)

(15, -4)

117.

$\left(2x-1\right)\left(3x+4\right)$

Find the equivalent expression.

a)

$6x^2-5x-4$

b)

$6x^2+5x-4$

c)

$6x+11x+4$

d)

$6x+5x-4$

e)

$6x^2-11x-4$

118.

What is vertex of the quadratic function x²+4x-21?

a)

(4, -21)

b)

(-2,-25)

c)

(2, -21)

d)

(4, -25)

119.

Find the Vertex:
y = x² + 6x + 2

a)

(-3,-7)

b)

(1,6)

c)

(6,2)

d)

No Real Solution

120.

What is the axis of symmetry in the function f(x) = (x-1)² +2

a)

x = 1

b)

x = -1

c)

x = 2

d)

x = -2

121.

Identify the extrema and the domain of the function y = -2(x+1)² + 4

a)

Max: 4, Domain: All Real Numbers

b)

Min: -4, Domain: All Real Numbers

c)

Max: 2, Domain: All real numbers when x is greater than 4

d)

Min: -2, Domain: All real numbers when x is less than 4

122.

Given the function $y=\left(x\pm h\right)^2+2$

what is the value of h?

a)

3

b)

-3

c)

2

d)

-2

123.

Given the equation $f\left(x\right)=2\left(x-2\right)^2\pm k$

What is the value of k?

a)

1

b)

2

c)

1.5

d)

2.5

124.

Which equation represents this graph.

a)

f(x)=(x - 4)² - 3

b)

f(x)=-(x - 4)² + 3

c)

f(x)=(x - 4)² + 3

d)

f(x)=-(x + 4)² + 3

125.

Match the equation with the graph:

a)

y = (x - 2)² + 4

b)

y = -(x - 4)² + 2

c)

y = -(x - 2)² + 4

d)

y = -(x + 2)² + 4

126.

Which of the following is the correct equation for the given graph?

a)

f(x) = (x - 2)² - 1

b)

f(x) = (x + 2)² - 1

c)

f(x) = -(x + 2)² - 1

d)

f(x) = -(x - 2)² - 1

127.

Which quadratic has COMPLEX roots?

a)

b)

c)

d)

128.

Describe the transformation from the parent graph

a)

Reflect over x, right 3, down 4

b)

Reflect over y, right 3, down 4

c)

Reflect over x, right 3, up 4

d)

Reflect over y, left 3, down 4

129.

Which quadratic function is represented by the graph?

a)

y = –(x – 4)² + 5

b)

y = –(x + 4)² + 5

c)

y = –2(x – 4)² + 5

d)

y = –2(x + 4)² + 5

e)

None of these

130.

1. Which of the following may represent the graph of $y=2x^2+8x+11$ ?

a)

b)

c)

d)

131.

What are the increasing and decreasing intervals for the function f(x) = (x+2)²-1?

a)

Increasing: (−∞, −2)

Decreasing: (−2, ∞)

b)

Increasing: (−2, ∞)

Decreasing: (−∞, -2)

c)

Increasing: (−1, ∞)

Decreasing: (−∞, -1)

d)

Increasing: (−∞, −1)

Decreasing: (−1, ∞)

132.

What are the increasing and decreasing intervals for the function: $g\left(x\right)=-2\left(x-3\right)^2+1$ ?

a)

Increasing: (−∞, 3)

Decreasing: (3, ∞)

b)

Increasing: (−∞, 1)

Decreasing: (1, ∞)

c)

Increasing: (2, ∞)

Decreasing: (-∞, 2)

d)

Increasing: (1, ∞)

Decreasing: (-∞, 1)

133.

What is the decreasing interval on the function shown?

a)

$\left(-\infty,\ 1\right)$

b)

$\left(-\infty,\ 2\right)$

c)

$\left(2,\ \infty\right)$

d)

$\left(1,\ \infty\right)$

134.

How many real and imaginary solutions does this graph have?

a)

one real solution

no imaginary solutions

b)

two real solutions

c)

two imaginary solutions

d)

one real solution

one imaginary solution

135.

How many real and imaginary solutions does the quadratic have?

a)

Two imaginary solutions

b)

One real solution

One imaginary solution

c)

Two real solutions

d)

One real solution

No imaginary solutions

136.

A rocket is launched in the air. The graph below shows the height of the rocket ℎ in meters after t seconds. Place the labels on the graph to show the characteristics of the graph.

a)

decreasing interval

b)

increasing interval

c)

Minimum

d)

Maximum

e)

x-intercept

f)

vertex

g)

x-intercept

h)

y-intercept

1

2

3

4

5

6

7

1)

2)

3)

4)

5)

6)

7)

137.

Write a quadratic function that represents a parabola that opens upward and has -intercepts (12 , 0) and (4 , 0).

a)

y = (x - 12)(x - 4)

b)

y = (x + 12)(x + 4)

c)

y = - (x - 12)(x - 4)

d)

y = - (x + 12)(x + 4)

138.

Write a quadratic function that represents a parabola that opens downward and has -intercepts (-5 , 0) and (1 , 0).

a)

y = (x + 5)(x - 1)

b)

y = (x - 5)(x - 1)

c)

y = - (x + 5)(x - 1)

d)

y = - (x - 5)(x - 1)

139.

Determine the axis of symmetry of the parabola with x intercepts ( -5, 0) and ( 7 , 0)

a)

x = 1

b)

x = 0

c)

x = -1

d)

x = 2

140.

A rocket is launched with a velocity equation given by
v = -4t²
Does the rocket reach a maximum or minimum velocity?

a)

maximum

b)

minimum

141.

The height of the ball after x seconds is given by the equation $f\left(x\right)=12x-0.8x^2$

What is the maximum height of the ball?

a)

7.5 feet

b)

7.5 seconds

c)

45 seconds

d)

45 feet

142.

What is the RANGE of the function

f\left(x\right)=\left(x+4\right)^2-1

a)

$\left(-4,\ \infty\right)$

b)

$\left(-\infty,\ \infty\right)$

c)

$\left(-1,\ \infty\right)$

d)

$\left(-\infty,\ -1\right)$

143.

What is the domain of this quadratic function?

a)

$\left(-\infty,\infty\right)$

b)

$\left[4,\ \infty\right)$

c)

$\left(-\infty,\ 2\right)$

d)

$\left(-\infty,\ 4\right]$

144.

What is the range of this quadratic function?

a)

\left(-\infty,\infty\right)

b)

$\left[4,\ \infty\right)$

c)

$\left(-\infty,4\right)$

d)

$\left(-\infty,\ 4\right]$

Algebra II Term Benchmark Study Guide

Total questions: 144

Worksheet time: 8hrs 31mins

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