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Ch. 9 Quadratic Functions

Total questions: 90

Worksheet time: 9hrs 37mins

Name
Class
Date
1.
Use the graph to determine the solutions.
a)
-1 and -3
b)
1 and -3
c)
1 and 3
d)
-1 and 3
2.
Does y = -4x2 have a maximum or minimum value?
a)
maximum
b)
minimum
3.
Does this graph in the back have maximum or minimum value?
a)
maximum
b)
minimum
c)
neither
d)
both
4.
What's the axis of symmetry of y=3x2-6x+4
a)
x=1
b)
x=-6
c)
x=2
d)
x=-1
5.
Does the equation open or or down? 
Y = -3x2 +7x - 2
a)
up
b)
down
6.
Does the equation have a max or min?
y = 2x2 + 7x + 5
a)
max
b)
min
7.
15f) Determine the line of symmetry.  y = x2+16x+64
a)
x=4
b)
x=2
c)
x=-8
d)
x=64
8.
The solutions of a quadratic equation are known as the _____.
a)
Vertices
b)
Roots
c)
Squares
d)
Formulas
9.
What is the axis of symmetry?
a)
the slope of the graph
b)
the dividing line for a parabola
c)
a way to spin my pencil
d)
the x-axis
10.
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
11.

Determine if the function graphed has a maximum or a minimum value and identify that value.

a)

maximum at -1

b)

minimum at -1

c)

maximum at 4

d)

minimum at 4

12.
What are the x- intercepts?
a)
x= 0 and x= -4
b)
x= 0 and x= 4
c)
y= 0
d)
x= 2
13.
Which answer choice describes  y = -3x2 +7x - 2 accurately?
a)
opens up with a maximum
b)
opens up with a minimum
c)
opens down with a maximum
d)
opens down with a minimum 
14.
How many solutions does this graph have?
a)
one
b)
two
c)
no solutions
d)
cannot be determined
15.
If the graph of a quadratic does not intercept the x-axis at any point, then it has:
a)
1 Real Solution
b)
2 Real Solutions
c)
Half a Solution
d)
No Real Solution
16.
What is another word for zeros?
a)
y-intercepts
b)
roots
c)
vertex
d)
axis of symmetry
17.
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
18.
What is the vertex of y=x2+4x+3?
a)
(2,1)
b)
(-2,1)
c)
(0,0)
d)
(-2,-1)
19.
What piece of information does c identify in the following equation?
y=ax2+bx+c
a)
Zeroes
b)
Axis of Symmetry
c)
Direction
d)
y-intercept
20.
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
21.
Find the y-intercept of
f(x) = 2x2-2x + 1

a)
2
b)
-2
c)
1
d)
-1
22.
When a basketball is shot, it forms an arc (also known as a parabola). When the basketball reaches it's highest point, what is that point called?
a)
Minimum value
b)
Slope
c)
Maximum value
d)
A parabola
23.
What are the x-intercepts?
a)
0 and 2
b)
-4 and 0
c)
2 and 3
d)
0 and 4
24.
Joe Mauer hits a fly ball.  You can track the height of the ball using the equation:   h(t) = -16t2 + 140t + 2  
What was the starting
                        height of the ball?                                                                                      
a)
-16 feet
b)
140 feet
c)
2 feet
d)
0 feet
25.
What is the range?
a)
y≥-3
b)
y≥-1
c)
All real numbers
d)
y≤-1
26.
What is the domain?
a)
-4<x<-2
b)
All Real Numbers
c)
-6<x<0
d)
y≥-1
27.
What is the vertex?
a)
-1
b)
-3
c)
(-3, -1)
d)
(-1, -3)
28.
In the expression 4x2-5x+9 the leading coefficient is
a)
9
b)
-5
c)
-4
d)
4
29.
What is the equation for the axis of symmetry?
a)
y=3
b)
x=3
c)
x=5
d)
x=1
30.
What is the green dot on the parabola called?
a)
maximum
b)
minumum
c)
roots
d)
zeros
31.
What is the vertex of the quadratic function:
y = x2 - 6x + 11?
a)
(3,2)
b)
(-3,-2)
c)
(-3,2)
d)
(3,-2)
32.
Determine the vertex of the parabola:
y = 5x2 - 20x + 13
a)
(5, -7)
b)
(-2, -7)
c)
(2, -7)
d)
(-7, -2)
33.
What is the formula to find the vertex of a parabola?
a)
x = -b/2
b)
x = -b
c)
x = -b / (2a)
d)
x = -b / 2
34.
The axis of symmetry line passes through which point?
a)
y-intercept
b)
any random point
c)
vertex
d)
none of these
35.
What is another name for the x-intercepts of a quadratic?
a)
y-intercepts
b)
zeros
c)
x-axis
d)
none of these
36.
The graph of a quadratic function is called
a)
a line
b)
a hyperbola
c)
a parabola
d)
a cubic
37.
Standard form of a quadratic equation
a)
y=x²
b)
y=ax²+bx+c
c)
y=mx+b
d)
y=x
38.
3x2 - 4 is a quadratic
a)
true
b)
false
39.
Which of the following is NOT a quadratic function
a)
f(x) = -3x2
b)
f(x) = -5x - x2
c)
y = 3x3 - 4x + 5
d)
A = pi.r2
40.
What are the green dots called?
a)
axis of symmetry
b)
vertex
c)
parabola
d)
roots or x-intercepts
41.
Does this parabola have a maximum or minimum?
a)
Maximum
b)
Minimum
42.
The formula x = -b/2a is used to find
a)
the roots
b)
the x-value of the vertex
c)
the y-intercept
d)
the axis of symmetry
43.
True or false:
The solution, root, x-intercept, and zero of a problem are all the same thing
a)
True
b)
False, because the solution and root are the same but the x-intercept and zero are different
c)
False, because the x-intercept and root are the same but the zero and solution are different
d)
False, they are all different
44.

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

a)

16

b)

-8

c)

8

d)

-24

45.
y=2x2-6x+1 is in what form?
a)
Vertex Form
b)
Factored form
c)
Standard Form 
d)
Cannot be determined
46.
.How many zeros does this parabola have? 
a)
3
b)
2
c)
0
d)
1
47.
Does the following quadratic equation have a maximum or minimum value? How can you tell?
y=x²+2x-3
a)
Minimum value, because the a value is positive
b)
Maximum value, because the b value is positive
c)
Maximum value, because the a value is positive
d)
Minimum value, because the c value is negative
48.
What is the domain of f(x)=x²-4 ?
a)
−∞ ≤ x ≤ +∞
b)
 x ≥ -4
c)
−∞ ≤ y ≤ +∞
d)
 y ≥ -4
49.
How many solutions does this graph have?
a)
one
b)
two
c)
no solutions
d)
cannot be determined
50.
How many solutions does this graph have?
a)
one
b)
two
c)
no solutions
d)
cannot be determined
51.
How many solutions does this graph have?
a)
one
b)
two
c)
no solutions
d)
cannot be determined
52.
Find the vertex of 
f(x) = -x2 - 4x + 12.
a)
(-2, 16)
b)
(2, 0)
c)
(2, 4)
d)
(-2, 4)
53.
Find the axis of symmetry for
f(x) = x2- 8x + 15.
a)
x = -4
b)
x = 4
c)
y = 4
d)
y = -4
54.
If the graph of a quadratic does not intercept the x-axis at any point, then it has:
a)
1 Real Solution
b)
2 Real Solutions
c)
Half a Solution
d)
No Real Solution
55.
What is the y intercept for the equation:
y = -8x2 + 3x - 7
a)
(0, -8)
b)
(0, 3)
c)
(-8, -7)
d)
(0, -7)
56.

A dolphin jumps from the water at at initial velocity of 16 feet per second. The equation h = -8t2 + 16t models the dolphin's height at any given time, t. What is the maximum height the dolphin jumps?

a)

1 foot

b)

5 feet

c)

7 feet

d)

8 feet

e)

12 feet

57.

You and some friends went to a haunted house on Halloween. The mummy scared one friend so much that she jumped into the air! The equation h = -4t2 + 2t models her jump where h is her jump's height in feet t seconds after the mummy scares her. When did she reach her maximum height?

a)

0.1 seconds

b)

0.25 seconds

c)

0.50 seconds

d)

1 second

e)

2 seconds

58.

Your nephew is standing on his deck, which is 4 feet off the ground. He tosses his toy up into the air. The equation

h = -2t2 + 7t + 4 models the toy's height, h, from the ground at t seconds after he threw it. How high is the toy after 1 second?

a)

2

b)

4

c)

9

d)

10

e)

15

59.

Fireworks are fired from the roof of a 100-foot building. The equation h = -16t2 +84t + 100 models the height, h, of the fireworks at any given time, t. How high do the fireworks get?

a)

2.625

b)

6.25

c)

100

d)

200

e)

210.25

60.

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

61.

Your friend passes you the ball during a soccer game. The height off the ground is modeled by the equation

h = -4t2 + 12t. How high did the soccer ball get?

a)

1.5

b)

3

c)

5

d)

9

e)

15

62.

Describe the transformations on

f(x) = x2 to produce g(x) = -5x2

a)

Shifted down, reflected across the x-axis, more wide

b)

Reflected across the x-axis, more wide

c)

Shifted down, more narrow

d)

Reflected across the y-axis, more narrow

e)

Reflected across the x-axis, more narrow

63.

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

64.

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

65.

Which of the following mean the same as x-intercept? (More than one answer! Select all that are correct)

a)

Zero

b)

Root

c)

Axis of Symmetry

d)

Solution

e)

Maximum

66.
If the blue is f(x)=x2, the 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
67.
If the blue 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
68.
How did we transform from the parent function?
y = x2 + 2
a)
horizontal shift up
b)
vertical shift up
c)
horizontal shift down
d)
vertical shift down
69.
Which transformation maps the graph of
f(x) = x2 to the graph of g(x) = (x + 4)2?
a)
horizontal shift right 4 units
b)
vertical shift up 4 units
c)
horizontal shift left 4 units
d)
vertical shift down 4 units
70.
a)
±72
b)
±12
c)
12
d)
No real solution
71.
a)
√3
b)
±√3
c)
-3
d)
No real solution
72.
a)
±81
b)
±9
c)
±3
d)
No real solution
73.
a)
±√9
b)
±3
c)
±1
d)
No real solution
74.
a)
±23.25
b)
±5
c)
±25
d)
No real solution
75.

In order to find the vertex of an equation in standard form, the first two steps are to use the equation _____ to find the x value, and then you can plug that value back into the equation to find the _____.

a)

-b/2a, y-value

b)

(x-h)^2, y-intercept

c)

(x-r1), solution

d)

ax^2, vertex

76.
a)
-4, 2
b)
-2, 4
c)
-16
d)
-4
77.
a)
-2, 4
b)
-8
c)
±8
d)
No real solution
78.
a)
-3, 4
b)
3, 4
c)
-4, -3
d)
-3
79.
a)
-6, -2
b)
-2, 6
c)
2, 6
d)
-6, 2
80.
a)
±1.5
b)
1.5
c)
±1
d)
No real solution
81.
Convert x2+6x+9 to factored form and identify the solution.
a)
(x+3)(x+3); x=-3
b)
(x+4)(x+5); x=-4, -5
c)
(x-3)(x-3); x=3
d)
Not factorable
82.
Convert x2-6x+9 to factored form and identify the solution.
a)
(x-3)(x-3); x=3
b)
(x+3)(x+3); x=-3
c)
(x+4)(x+2); x=-4, -2
d)
Not factorable
83.
Convert x2-9x+20 to factored form and solve.
a)
(x-10)(x+2); x=-2, 10
b)
(x+4)(x+5); x=-5, -4
c)
(x-4)(x-5); x=4, 5
d)
Not factorable
84.
Factor x2-6x-40
a)
(x-10)(x+4)
b)
(x+10)(x-4)
c)
(x-8)(x+5)
d)
(x+8)(x-5)
85.
Solve
x2 + 13x + 12 = 0
a)
x = -12, -1
b)
x = 12, 1
c)
x = 13, 1
d)
x = -13, -1
86.
What should you do first in solving this equation?
x2 + 6x - 13 = 3
a)
Get factored form
b)
Write down: a=1, b=6, c=-13
c)
Make it equal 0 by subtracting 3 on each side
d)
Type it all in a calculator.
87.
Solve the equation: 
5x2 - 35x + 60 = 0
a)
x = 3,  -4
b)
x = -3,  4
c)
x = 3,  4
d)
x = -3,  -4
88.
Solve the equation:
4x2+2x - 6 = 0
a)
x = 1 & -1.5
b)
x = -1 & 1.5
c)
x = (-2 ±√92)/8
d)
x = (-2 ± √100)/8
89.
Factor x2-11x+24
a)
(x-3)(x-8)
b)
(x-2)(x-12)
c)
(x+3)(x+8)
d)
(x+2)(x+12)
90.

What are the solutions for the equation 2x2 + 16x = 18

a)

x = -1 and x = 9

b)

x = -9 and x = 1

c)

x = 2 and x= 18

d)

x = 2 and x = 16

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