Free Printable Unit 2 Review

1.

Which transformation transforms the graph of
f(x) = x² to the graph of
g(x) = (x + 4)²?

a)

a vertical translation 4 units up

b)

a vertical translation 4 units down

c)

a horizontal translation 4 units to the left

d)

a horizontal translation 4 units to the right

2.

How did we transform from f(x) =x²

to

g(x) = -3x²

a)

reflection in x-axis and vertical shift down

b)

reflection in x-axis and vertical stretch

c)

horizontal stretch

d)

reflection in x-axis and vertical compression

3.

If the blue graph is
f(x) = x²the red must be...

a)

g(x) = (x + 3)²

b)

g(x) = (x - 3)²

c)

g(x) = x²+ 3

d)

g(x) = x²- 2

4.

Does the quadratic have a max/min vertex, and does the graph open up/down?

a)

max/ opens down

b)

min/ opens up

c)

max/ opens up

d)

min/ opens down

5.

Find the equation of the parabola that has moved...

3 units up

a)

$y=x^2+3$

b)

$y=x^2-3$

c)

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

d)

$y=3x^2$

6.

Find the equation of the parabola that has...

moved 3 units to the left

moved 5 units up

a)

$y=\left(x+3\right)^2+5$

b)

$y=\left(x+5\right)^2+3$

c)

$y=\left(x-3\right)^2+5$

d)

$y=\left(x+5\right)^2-3$

7.

Which function has a translation of 2 units right and a vertical stretch by a factor of 5?

a)

f(x)= 5(x - 2)²

b)

f(x) = 5(x + 2)²

c)

f(x) = (x - 2)² - 5

d)

f(x) = (x + 2)² + 5

8.

What is the correct equation for this parabola?

a)

$y=\left(x-3\right)^2-1$

b)

$y=\left(x-3\right)^2+1$

c)

$y=\left(x+3\right)^2-1$

d)

$y=\left(x+3\right)^2+1$

9.

What is the name of this form:
y = ax² + bx + c

a)

vertex form

b)

standard form

c)

factored form

d)

zero form

10.

Where is the axis of symmetry for this parabola?

a)

x = −1

b)

x = 0

c)

y = 3

d)

x = −3

11.

What is the axis of symmetry?
f(x) = x²- 8x + 15.

a)

x = -4

b)

x = 4

c)

y = 4

d)

y = -4

12.

Does the equation open up or down?
Y = -3x² +7x - 2

a)

up

b)

down

c)

Neither; it opens to the right.

d)

Neither; it opens to the left.

13.

What is the "formula" for finding the axis of symmetry?

a)

$y=ax^2+bx+c$

b)

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

c)

$y=mx+b$

d)

$x=\frac{-b\pm\sqrt{b^2-4ac}}{2a}$

14.

Find the vertex y = x² - 2x - 5

a)

(-2, 10)

b)

(-1, 15)

c)

(1, -6)

d)

(1, -12)

15.

Quadratic equations take the shape of a _______ when graphed.

a)

parabola

b)

straight line

c)

snaked line

d)

elliptical

16.

A parabola has a vertex at (-3,2).

What is the axis of symmetry?

a)

y = -2

b)

x = 3

c)

x = -3

d)

y = 2

17.

What is the domain and the range for the graph?

a)

$D:\ \left(-\infty,+\infty\right)$ $R:\ \left[0,4\right]$

b)

$D:\ \left(-\infty,+\infty\right)$

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

c)

$D:\ \left(-\infty,+\infty\right)$

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

d)

$D:\ \left[-2,2\right]$

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

18.

Does y = -4x² +8

have a maximum or minimum value?

a)

maximum

b)

minimum

19.

What is the axis of symmetry for the following equation?
y=4x²-8x+9

a)

x=-8

b)

x=1

c)

x=-1

d)

x=2

20.

Find the vertex of y = -x²- 4x + 12

a)

(-2, 16)

b)

(2, 0)

c)

(2, 4)

d)

(-2, 4)

21.

Factor: 3v² - 8v + 5

a)

(3v + 5)(v - 1)

b)

(3v - 5)(v + 1)

c)

(3v - 5)(v - 1)

d)

(3v + 5)(v + 1)

22.

Factor 4x² - 81

a)

(4x - 9)(x + 9)

b)

(2x - 9)(2x + 9)

c)

(2x - 9)(2x - 9)

d)

(4x - 1)(x + 81)

23.

Factor $k^2-2k-24$

a)

$(k-4)(k+6)$

b)

$(k+4)(k+6)$

c)

$(k+6)(k-1)$

d)

$(k+4)(k-6)$

24.

Which of the following is a name for the answer to a quadratic equation?

a)

Vertex

b)

Root

c)

Zero

d)

Quartic

e)

x - intercept

25.

x²+4x-32=0

a)

x= -8, 4

b)

x= 8, -4

c)

x= -8, -4

26.

Solve
2x² + 7x - 15 = 0

a)

-1.5 or 5

b)

No Solution

c)

-5 or 1.5

d)

0.7 or 5

27.

What is the discriminant?

a)

$b^2$

b)

$-b\pm\sqrt[]{b^2}-4ac$

c)

$b^2-4ac$

d)

$2a$

28.

Which answer is the value of the discriminant for $2x^2+3x-4=0$ ?

a)

$41$

b)

$-23$

c)

$\sqrt[]{41}$

d)

$23$

29.

What is another name for the x-intercepts of a quadratic?

a)

y-intercepts

b)

zeros

c)

x-axis

d)

none of these

30.

$x^2+12x\ +\ \ ?$

What value completes the square?

a)

3

b)

6

c)

12

d)

36

31.

$x^2-7x=0$

Solve by the method of your choice.

a)

x = 7 only

b)

x = 0 only

c)

x = 0 and 7

d)

There is no real answer for this equation.

32.

$3x^2-10x+1=0$

Solve by the method of your choice.

a)

$x=\frac{-10\pm\sqrt{88}}{6}$

b)

$x=\frac{-5\pm2\sqrt{22}}{3}$

c)

$x=\frac{10\pm\sqrt{112}}{6}$

d)

$x=\frac{5\pm\sqrt{22}}{3}$

33.

$2x^2=8x+3$

Step 1:

$2x^2-8x-3=0$

Step 2:

$x=\frac{8\pm\sqrt{64-4\left(2\right)\left(-3\right)}}{4}$

Step 3:

$x=\frac{8\pm\sqrt{40}}{4}$

Step 4:

$x=\frac{8\pm2\sqrt{10}}{4}$

Step 5:

$x=\frac{4\pm\sqrt{10}}{2}$

Suzanne solved the equation using this process.

Did she make a mistake?

If yes, at which line did she make her first mistake?

(There are 5 steps in her process)

a)

Suzanne made no errors.

b)

Step 2

c)

Step 3

d)

Step 4

e)

Step 5

34.

What is the color of the graph that has exactly one real zero?

a)

black

b)

green

c)

purple

d)

red

e)

None of these graphs has exactly one zero.

35.

What is the color of the graph that has no real zeros?

a)

black

b)

green

c)

purple

d)

red

e)

None of these graphs have no real zeros

36.

When using factoring to solve a quadratic equation, what must be true?

a)

The equation must be set equal to 1.

b)

The equation must be set equal to 10.

c)

The equation must be set equal to 0.

d)

It is not necessary to set the equation equal to anything.

37.

Use the quadratic formula to find the solutions for

y = -x² - 5x + 12

a)

No Real Solution

b)

c)

d)

38.

What is one of the solutions to this equation?

(x - 3)² = 49

a)

7

b)

-7

c)

-4

d)

4

39.

$f\left(x\right)=x^2-16x+43$

Complete the square and find the zeros

a)

$x=-16\pm\sqrt{21}$

b)

$x=16\pm\sqrt{21}$

c)

$x=-8\pm\sqrt{21}$

d)

$x=8\pm\sqrt{21}$

40.

3 For the function above, is the discriminant positive, negative, or zero?

a)

Positive

b)

Negative

c)

Zero

41.

(3 + 8i)(-2 - i)

a)

2-19i

b)

23-i

c)

34+5i

d)

23-i

42.

Simplify.

a)

b)

c)

d)

43.

Simplify i²³

a)

i

b)

-1

c)

1

d)

-i

44.

a)

A

b)

B

c)

C

d)

D

45.

The expression (2 + 3i)² is equal to

a)

-5

b)

-5 + 12i

c)

13

d)

13 + 12i

46.

Simplify: i³¹

a)

i

b)

-i

c)

1

d)

-1

47.

(3 + 2i) + (4 - 5i)

a)

7 + 7i

b)

1 - 3i

c)

1 - 7i

d)

7 - 3i

48.

(4 - 2i) - (3 + 6i)

a)

7 - 4i

b)

1 + 4i

c)

1 - 8i

d)

7 - 8i

49.

For that same projectile, at what TIME does the maximum height occur?
h(t) = -16t² + 20t + 6

a)

0 seconds

b)

.625 seconds

c)

160 seconds

d)

2 seconds

50.

An object in launched directly upward at 64 feet per second (ft/s) from a platform 80 feet high. Its height is represented by the equation
s(t) = –16t² + 64t + 80.
What will be the object's maximum height?

a)

2 ft

b)

80 ft

c)

144 ft

d)

64 ft

51.

A lizard is jumping across the water in search of food. The equation h = -12t² + 6t models the lizard's height in feet above the water t seconds after he jumps. How long after jumping is he back on the water?

a)

0.1 seconds

b)

0.25 seconds

c)

0.50 seconds

d)

0.75 seconds

e)

1 second

52.

A tennis ball is hit upwards and its height h(t) in meters after t seconds is given by $h(t)=-5t^2+30t+2$ What is the initial height of the tennis ball?

a)

2 m

b)

30 m

c)

5 m

d)

0 m

53.

The function f(t) = -5t²+20t + 60 models the approximate height of an object t seconds after it is launched. How many seconds does it take the object to hit the ground?

a)

4 seconds

b)

-2 seconds

c)

6 seconds

d)

9 seconds

54.

If the discriminant is positive, then the solution will be

a)

one real solution

b)

two real solutions

c)

no real solutions

d)

one imaginary solution

55.

1 What does the discriminant tell us?

a)

The maximum or minimum

b)

The y-intercept

c)

The number and type of solutions

d)

The axis of symmetry

56.

2 A function has a discriminant of 0.

How many x-intercepts does it have?

a)

0

b)

1

c)

2

d)

5

57.

A function has a discriminant of -3.
______________
How many x-intercepts does it have?

a)

0

b)

1

c)

2

d)

3

58.

Make a true statement about about Graph B

The discriminant is (a)

There will be (b)

Choose from the below words

negative

two complex solutions

positive

zero

one real solution

two real solutions

Unit 2 Review

Total questions: 58

Worksheet time: 3hrs 14mins

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