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Quadratics Review

Total questions: 54

Worksheet time: 3hrs 49mins

Name
Class
Date
1.

Identify the domain and range of the quadratic function.

a)

Domain: -6 ≤ x ≤ 2

Range: -3 ≤ y ≤ 5

b)

Domain: All real number

Range: -3 ≤ y ≤ 5

c)

Domain: All real numbers

Range: y ≥ -3

d)

Domain: All real number

Range: y ≤ -3

2.
Which of the following describes the graph of f(x)= x2 - 2x -15.
a)
The graph has a maximum and has the x-intercepts of (-3, 0) and (5, 0)
b)
The graph has a minimum and has the x-intercepts of (-3, 0) and (5, 0)
c)
The graph has a maximum and has the x-intercepts of (3, 0) and (-5, 0)
d)
The graph has a minimum and has the x-intercepts of (3, 0) and (-5, 0)
3.
Which if the following is an equation for a quadratic function that opens downward and has the vertex of (-4, 7)?
a)
f(x)= -(x-4)2+7
b)
f(x)= (x+4)2+7
c)
f(x)= -(x+4)2+7
d)
f(x)= (x-4)2+7
4.
Factor
x2 + 9x - 36
a)
(x + 12)(x - 3)
b)
(x + 9)(x - 4)
c)
(x - 12)(x + 3)
d)
(x - 9)(x - 4)
5.
Factor
n2 + 5n - 6
a)
(n - 2)(n - 3)
b)
(n - 1)(n + 6)
c)
(n + 1)(n - 6)
d)
(n + 2)(n - 3)
6.
Factor
r2 -16r + 60
a)
(r - 15)(r + 4)
b)
(r - 6)(r + 10)
c)
(r - 6)(r - 10)
d)
(r +30)(r - 2)
7.
Factor:
v2 + 3v - 88
a)
(v + 11)(v - 8)
b)
(v + 22)(v - 4)
c)
(v + 8)(v - 11)
d)
(v - 22)(v + 4)
8.
Factor completely.
5x2 - 7x + 2
a)
5(x - 2)(x + 1)
b)
(5x - 2)(x + 1)
c)
(7x - 1)(x - 4)
d)
(5x - 2)(x - 1)
9.
Factor completely.
2n2 + 17n - 30
a)
(2n - 3)(n + 10)
b)
(2n - 3)(n - 10)
c)
(2n + 3)(n - 10)
d)
(5n - 6)(n + 5)
10.
Factor completely.
5x2 - 13x + 6
a)
(x - 3)(5x - 2)
b)
(5x - 3)(x - 2)
c)
5(x - 3)(x + 2)
d)
Not factorable
11.
Factor completely.
3x2 + 10x - 8
a)
(3x + 2)(x + 4)
b)
(7x + 5)(x + 2)
c)
(3x - 2)(x + 4)
d)
(7x - 3)(x - 4)
12.
Factor:
 2m² + 3m - 9
a)
2(m + 3)(m - 3)
b)
(2m - 3)²
c)
(m + 3)(2m - 3)
d)
(2m + 3)(m - 3)
13.
Factor completely: 
3x2 + 18x +15
Hint: Factor GCF first.
a)
3(x2 + 6x + 5)
b)
(x + 5)(x + 1)
c)
3(x + 5)(x + 1)
d)
Prime
14.
Factor Completely:  5v2 - 30v + 40
a)
(5v - 8)(v + 5)
b)
(5v + 5)(v - 8)
c)
5(v - 4)(v - 2)
d)
5(v + 8)(v - 5)
15.
2x2 + 6x - 56
a)
2(x - 7)(x + 4)
b)
(2(x + 7)(x - 4)
c)
(2x + 14)(x - 4)
d)
(x + 7)(2x - 8)
16.
Factor:
y2 + 2y - 35
a)
(y + 5)(y - 7)
b)
(y - 5)(y - 7)
c)
(y +7)(y - 5)
d)
(y + 5)(y + 7)
17.
What are the green dots called?
a)
axis of symmetry
b)
vertex
c)
parabola
d)
roots or x-intercepts
18.
What is the equation for this parabola in factored form?
a)
y=(x+2)(x-1)
b)
y=(x-2)(x+1)
c)
y=(x-2)(x-1)
d)
y=(x+2)(x+1)
19.
A parabola is upside-down when a is:
a)
negative
b)
positive
c)
0
d)
infinite
20.
|v + 8| − 5 = 2 
a)
{-1,-15}
b)
{-1,-5}
c)
{-15,15}
d)
No Solution
21.
−2|−2r − 4| = -12
a)
{3,1}
b)
{-3,-1}
c)
{-3}
d)
No Solution
22.

Identify the 'b' value: y = 16x2 -8x -24

a)

16

b)

-8

c)

8

d)

-24

23.
y=2x2-6x+1 is in what form?
a)
Vertex Form
b)
Factored form
c)
Standard Form 
d)
Cannot be determined
24.
A quadratic equation creates a... 
a)
v-shaped graph 
b)
a straight line
c)
a parabola 
d)
a vertical line
25.
What form is this?
f(x)= 2(x+3)2 - 4
a)
factored form
b)
Standard Form
c)
Vertex Form
d)
Parabola
26.
Does f(x) = -3x2 +15x - 4 open up or open down?
a)
opens up
b)
opens down
27.
Solve Using the Quadratic Formula
 x2 + 4x - 40 = -8
a)
-10 & -4
b)
-4 & 10
c)
-8 & 4
d)
8 & -4
28.
Solve Using the Quadratic Formula 
2x2 + 7x - 15 = 0
a)
-1.5 or 5
b)
No Solution
c)
-5 or 1.5
d)
0.7 or 5
29.

Determine the values of a, b, and c for the quadratic equation:

4x2 – 8x = 3

a)

a = 4, b = -8, c = 3

b)

a = 4, b =-8, c =-3

c)

a = 4, b = 8, c = 3

d)

a = 4, b = 8, c = -3

30.

What should you do first in solving this equation?

x2 + 6x - 13 = 3

a)

Factor

b)

Write down: a = 1, b = 6, c = -13

c)

Subtract 3 from both sides.

d)

Add 3 to both sides.

31.
Multiply:
(3x – 1)(x + 5) 
a)
3x2 + 4x + 5
b)
3x2 + 4x - 5
c)
3x2 + 14x + 5
d)
3x2 + 14x - 5
32.
Simplify:
(x - 9)(x - 7)
a)
x2 - 2x - 63
b)
x2 - 16x - 63
c)
x2 - 2x + 63
d)
x2 - 16x + 63
33.
Which of the following shows
f(x) = x2 + 12x - 2
written in vertex form?
a)
f(x) = (x + 6)2 + 142
b)
f(x) = (x + 6)2 - 34
c)
f(x) = (x + 6)2 - 38
d)
f(x) = (x + 6)2 + 34
34.
Which of the following forms are best to use if we want to identify the vertex of a quadratic equation?
a)
Standard Form
b)
Vertex Form
c)
Intercept Form
35.

Convert the equation from vertex form (shown) to standard form:

y = -3(x + 5)2 - 4

Formula: y = ax2 + bx + c

a)

y = 9x2 - 15x + 21

b)

y = -3x2 - 75x - 4

c)

y = 9x2 + 90x + 221

d)

y = -3x2 - 30x - 79

36.
What transformations have occurred? 
a)
Right 2 and up 2
b)
Left 2 and up 2
c)
Right 2 and down 2
d)
Left 2 and down 2
37.
Describe the transformation of y = (x - 4)2
a)
Shift UP
b)
Shift DOWN
c)
Shift LEFT
d)
Shift RIGHT
38.
Describe the transformation of y = x2 + 4
a)
Shift UP
b)
Shift DOWN
c)
Shift LEFT
d)
Shift RIGHT
39.
Compare the function y = 0.3x2 to the parent function y = x2
a)
Wider
b)
Narrower
40.
Compare the function y = 5x2 to the parent function y = x2
a)
Wider
b)
Narrower
41.
Describe the transformation of y = 3(x - 3)2 + 3
a)
Narrow, Right, Up
b)
Narrow, Left, Down
c)
Wide, Right, Up
d)
Wide, Left, Down
42.

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

43.

Your cousin hit a golf ball with an initial velocity of 27 feet per second. The equation h = -6t2 + 27t models the golf ball's height in feet t seconds after the ball was hit. How long after being hit did the ball reach maximum height?

a)

1 second

b)

2.25 seconds

c)

3 seconds

d)

4.5 seconds

e)

5 seconds

44.

A frog is sitting on the ground when he is scared by a big dog. The movement of the frog is modeled by the equation

h = -6t2 + 6t where h is the frog's height at any given time, t. How high does the frog jump?

a)

0.5

b)

1

c)

1.5

d)

2

e)

5

45.

A toy rocket is launched from the top of a 48-foot hill. The rocket's height, h(x), is modeled by the

equation h(x) = -16x2 + 32x +48 after x seconds. How high was the rocket at 2 seconds?

a)

3

b)

32

c)

48

d)

64

e)

100

46.

Heather dropped a water balloon over the side of her school building from a height of 80 feet. The approximate height of the balloon at any point during its fall can be represented by the following quadratic equation:

h = -16t2 + 80

About how long did it take for the balloon to hit the ground?

a)

1.73 seconds

b)

2.24 seconds

c)

2.45 seconds

d)

2.83 seconds

47.

Jason launched a rocket for a physics experiment. This equation can be used to find the height (h), in feet, of the rocket after t seconds.

h = -16t2 + 288t + 8

How many seconds will it take for the rocket to reach a height of 1,304 feet?

a)

9.0 seconds

b)

9.6 seconds

c)

81.0 seconds

d)

82.0 seconds

48.
Convert
 f(x) = 3(x - 5)2 - 1 
to standard form.
a)
f(x) = 3x2 -30x + 74
b)
f(x) = 3x2 -10x + 24
c)
f(x) = 3x2 -30x + 24
d)
f(x) = 3x2 -30x + 75
49.
Convert
 f(x) = 2(x - 2)2 +9
to standard form.
a)
f(x) = 2x2 + 8x + 9
b)
f(x) = 2x2 - 8x - 4
c)
f(x) = 2x2 - 8x + 17
d)
f(x) = 2x2 - 8x + 8
50.
What is the y-intercept of 
f(x)=2x2 + 4x + 6
a)
(6 , 0)
b)
(-6 , 0)
c)
(0, -6)
d)
(0 , 6)
51.
Which of the following equations matches standard form of a quadratic?
a)
ax + by = c
b)
y = a(x - h)2 + k
c)
y = ax2 + bx + c
d)
y = mx + b
52.
Which equation has a vertex of (-3, 4)?
a)
y = 2(x+3)2 + 4
b)
y = (x+3)2 - 4
c)
y = (x-3)2 + 4
d)
y = 2(x - 3)2 + 4
53.
Does this graph have a maximum or minimum value?
a)
maximum
b)
minimum
c)
neither
d)
both
54.
What is the vertex?
a)
(2, 4)
b)
(3, -1)
c)
(0, 8)
d)
(4, 2)

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