Free Printable Unit 5 test review

1.

Which graph matches the equation shown?

$g\left(x\right)=2x^2-4x$

a)

b)

c)

d)

2.

Which graph matches the equation shown?

$g\left(x\right)=\frac{1}{2}\left(x+3\right)\left(x-1\right)$

a)

b)

c)

d)

3.

Which graph matches the equation shown?

$g\left(x\right)=2\left(x+1\right)^2+2$

a)

b)

c)

d)

4.

Which graph matches the equation shown?

$g\left(x\right)=2x^2-4x+4$

a)

b)

c)

d)

5.

If a soccer player kicks a ball and it reaches a maximum height of 8 feet after traveling for 20 yards, how far downfield does the ball land?

a)

4 Yards

b)

10 Yards

c)

16 Yards

d)

40 Yards

6.

What is the vertex of a parabola when the equation is:

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

a)

(1,-4)

b)

(1,4)

c)

(2,-1)

d)

(-1,-4)

7.

What is the axis of symmetry of the parabola given by this equation?

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

a)

x=4

b)

x=1

c)

x=-4

d)

x=-1

8.

What is the y-intercept of this equation?

$g\left(x\right)=x^2+8x+16$

a)

(16,0)

b)

(8,0)

c)

(0,16)

d)

(0,8)

9.

What are the x-intercepts of this equation?

$h\left(x\right)=-\frac{2}{3}\left(x+1\right)\left(x-5\right)$

a)

(1,5) and (2,3)

b)

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

c)

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

d)

1 and 5

10.

How long was the rocket in the air?

a)

3 seconds

b)

5 seconds

c)

9 seconds

d)

6 seconds

11.

Write the equation $y=2\left(x-1\right)^2+1$ in standard form

12.

Write the equation in intercept form $y=x^2-7x+10$

(a)

13.

Graph the quadratic inequality

14.

graph the system of inequalities

15.

Which equation would shift the quadratic function

f\left(x\right)=x^2

up 3 units and to the right 4 units.

a)

$f\left(x\right)=\left(x+3\right)^2+4$

b)

$f\left(x\right)=3\left(x-4\right)^2$

c)

$f\left(x\right)=\left(x-4\right)^2+3$

d)

$f\left(x\right)=\left(x+4\right)^2+3$

16.

Describe the transformation:

f\left(x\right)=\left(x+3\right)^2-2

a)

right 3, down 2

b)

up 3, left 2

c)

left 3, up 2

d)

left 3, down 2

17.

Write an equation of a quadratic that is translated down 2 units.

a)

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

b)

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

c)

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

d)

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

18.

Given f(x) = (x + 6)² - 2 , how did we transform from the parent function?

a)

Horizontal shift left 6, vertical shift up 2

b)

Horizontal shift left 6, vertical shift down 2

c)

Horizontal shift right 6, vertical shift down 2

d)

Horizontal shift right 6, vertical shift up 2

19.

Given $f\left(x\right)=\frac{1}{4}x²$ how did we transform from the parent function?

a)

Vertical compression (wider)

b)

Vertical stretch (narrower)

c)

Vertical compression (wider) and reflection over x-axis

d)

Vertical stretch (narrower) and reflection over x-axis

20.

Identify the vertex and whether the graph opens up or down.

a)

(5, 2); opens up

b)

(5, 2); opens down

c)

(-5, 2); opens up

d)

(-5, 2); opens down

21.

a)

$y=1.6x^2+5.6x$

b)

$y=1.6x^2-5.6x$

c)

$y=-0.7x^2+8.1x+5.3$

d)

$y=-0.7x^2+8.1x-5.3$

22.

Use the given points to find the equation of the line of best fit (regression equation).

Enter your answer as y=ax^2+bx+c

23.

Write the equation of the graph in vertex form

a)

$y=x^2-2x$

b)

$y=1\left(x-2\right)^2$

c)

$y=1\left(x+2\right)^2$

d)

$y=x^2-2$

24.

Write the equation of the graph in standard form

a)

$y=x^2-2$

b)

$y=-2x^2$

c)

$y=2x^2$

d)

$y=2x^2-1$

25.

What are the
x-intercepts of the function
f(x)= (x - 2)(x + 3)?

a)

x = - 2 or x = 3

b)

x = 2 or x = -3

c)

The are no real roots

d)

x = 2 or x = 3

26.

Does this graph in the back have maximum or minimum value?

a)

maximum

b)

minimum

c)

neither

d)

both

27.

Complete the square for
x² + 12x + ____

a)

x² + 12x + 144

b)

x² + 12x + 36

c)

x² + 12x - 36

d)

x² + +12x - 144

28.

Which equation best represents the graph?

a)

y = 2(x - 4)² + 5

b)

y = 2(x + 4)² + 5

c)

y = -2(x - 4)² + 5

d)

y = -2(x + 4)² + 5

29.

Find the zeros.

a)

0 and 4

b)

0 and -4

c)

0

d)

-4

30.

What are the values of the constants a, b, and c in the given function?

$f\left(x\right)=2x^2-3x+4$

a)

a = 2; b = 3; c = 4

b)

a = 2; b = -3; c = 4

c)

a = 2; b = -3; c = -4

d)

cannot be determined

31.

What is the opening of the given quadratic function?

(a)

32.

What property of quadratic function that the arrow points to?

(a)

33.

What property of quadratic function that the arrow points to?

(a)

34.

Which of the following is the correct formula in determining the vertex of the quadratic function?

a)

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

b)

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

c)

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

d)

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

35.

$f\left(x\right)=-2x^2+8x-7$

Determine the vertex of the given quadratic function.

(a)

36.

$f\left(x\right)=-2x^2+8x-7$

What is the domain of the given quadratic function?

a)

all real values of x

b)

all real values of y

c)

depends on the opening

d)

cannot be determined

37.

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

What is the vertex of the given quadratic function?

a)

V(0,k)

b)

V(h,0)

c)

V(h,k)

d)

V(k,h)

38.

What is the vertex of

f(x) = 2(x - 5)² + 12

a)

(-5, -12)

b)

(5,-12)

c)

(5, 12)

d)

(-5, 12)

39.

If the blue graph is
f(x) = x²
then the red must be...

a)

g(x) = x²- 5

b)

g(x) = x²+ 5

c)

g(x) = (x - 5)²

d)

g(x) = (x + 5)²

40.

A parabola has a vertex at (-3,2). Where is the axis of symmetry?

a)

y = -2

b)

x = 3

c)

x = -3

d)

y = 2

41.

Find the maximum or the minimum value of $f(x)=2x^2+3x-5$

a)

Minimum

$-\frac{49}{8}$

b)

Maximum

$-\frac{49}{8}$

c)

Minimum

$0$

d)

Maximum

$0$

42.

Find the range of $f(x)=-x^2+4x-5$

a)

$(-;-1]$

b)

$\left[-1;+\propto\right)$

c)

$(-;2]$

d)

$(-;-5]$

43.

Find the axis of symmetry of the graph of $f(x)=-2x^2-x-2$

a)

$x=-\frac{1}{4}$

b)

$x=\frac{1}{4}$

c)

$x=\frac{3}{4}$

d)

$x=-\frac{3}{4}$

44.

What are the
x-intercepts of the function
f(x)= (x - 2)(x + 3)?

a)

x = - 2 or x = 3

b)

x = 2 or x = -3

c)

The are no real roots

d)

x = 2 or x = 3

45.

The profit from selling local ballet tickets depends on the ticket price. Using past receipts, we find that the profit can be modeled by the function:

$p=-15x^2+600x+60$

What is the maximum profit you can make from selling tickets?

a)

$\$606$

b)

$\$6060$

c)

$\$60$

d)

$\$6$

46.

A ball is thrown into the air with an upward velocity of 40ft/s. Its height h in feet after t seconds is given by the function :

$h(t)=-16t^2+40t+10$

How many seconds does it take the ball to reach its maximum height?

a)

1.5

b)

2.5

c)

2.25

d)

1.25

47.

(a)

48.

a)

A

b)

B

c)

C

d)

D

49.

a)

I and II only

b)

I and III only

c)

II and III only

d)

I, II, and III

50.

a)

A

b)

B

c)

C

d)

D

51.

a)

F

b)

G

c)

H

d)

J

52.

a)

F

b)

G

c)

H

d)

J

53.

a)

F

b)

G

c)

H

d)

J

54.

a)

A

b)

B

c)

C

d)

D

55.

(a)

56.

a)

F

b)

G

c)

H

d)

J

57.

Use the graph to determine the solutions.

a)

-1 and -3

b)

1 and -3

c)

1 and 3

d)

-1 and 3

58.

Does y = -4x² have a maximum or minimum value?

a)

maximum

b)

minimum

59.

What is the domain of the function?
*Hint: Domain is the set of all x-values included in the function.

a)

x≥3

b)

x≤3

c)

All real numbers

d)

-1≤x≤5

60.

What is the range of the function?

*Hint: Range is all of the y-values included in the function.

a)

$-\infty<y\le3$

b)

$-3\le y<\infty$

c)

All real numbers

d)

-6≤y≤3

Unit 5 test review

Total questions: 60

Worksheet time: 1hrs 24mins

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