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WorksheetsGraphing Quadratics
Total questions: 82
Worksheet time: 3hrs 33mins
Name
Class
Date
1.
Which of these is a quadratic function?
a)
f(x) = 2x + 4
b)
f(x) = 2x
c)
f(x) = 3x2
d)
f(x) = 3x3 + 2x2 + 9
2.
True or false:
The solution, root, x-intercept, and zero of a problem are all the same thing
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
3.
Identify the 'b' value:
y = 16x2 -8x -24
y = 16x2 -8x -24
a)
16
b)
-8
c)
8
d)
-24
4.
What are the x- intercepts?
a)
(0,0) and (0,4)
b)
(0,0) and (4,0)
c)
x=2
d)
(2, –2)
5.
Which answer choice describes
y = –3x2 +7x – 2 accurately?
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
6.
.How many zeros does this parabola have?
a)
3
b)
2
c)
0
d)
1
7.
Does the following quadratic equation have a maximum or minimum value? How can you tell?
y=x²+2x-3
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
8.
How many solutions does this graph have?
a)
one
b)
two
c)
no solutions
d)
cannot be determined
9.
How many solutions does this graph have?
a)
one
b)
two
c)
no solutions
d)
cannot be determined
10.
What is the arrow pointing at? How can you use this value?
a)
The y-intercept. The x-value is the axis of symmetry and the y-value of this point is equivalent to the maximum/minimum
b)
The vertex. The x value of this point is equivalent to the maximum/minimum and the y-value is the axis of symmetry
c)
The x-intercept. The y value of this point is equivalent to the maximum and the x value is equivalent to the minimum
d)
The vertex. The x-value is the axis of symmetry and the y-value is equivalent to the minimum/maximum
11.
What is the equation for axis of symmetry?
a)
y=3
b)
x=3
c)
x=5
d)
x=1
12.
What are the green dots called?
a)
axis of symmetry
b)
vertex
c)
y-intercepts
d)
roots or x-intercepts
13.
What is the green dot on the parabola called?
a)
maximum
b)
minumum
c)
roots
d)
zeros
14.
Does this parabola have a maximum or minimum?
a)
Maximum
b)
Minimum
15.
Does this parabola have a minimum or maximum and what is its value?
a)
minimum: 2
b)
maximum: 2
c)
minimum: 5
d)
maximum: 5
16.
The vertex of this parabola is...
a)
(-4, -12.5)
b)
(12.5, 4)
c)
(-12.5, -4)
d)
(4, 12.5)
17.
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)
Zero
b)
y-intercept
c)
Maximum
d)
Minimum
18.
A parabola is upside-down when a is:
a)
negative
b)
positive
c)
0
d)
infinite
19.
What is the green dashed line called?
a)
roots or x-intercepts
b)
parabola
c)
axis of symmetry
d)
vertex
20.
The vertex of this graph is at.....
a)
(2,4)
b)
none of these
c)
(2.25,2.9)
d)
(0,0)
21.
The graph of a quadratic function is called a
a)
Parabola
b)
Vertex
c)
Axis of Symmetry
d)
Vertex Form
22.
Find the vertex of
f(x) = -x2 - 4x + 12
f(x) = -x2 - 4x + 12
a)
(-2, 16)
b)
(2, 0)
c)
(2, 4)
d)
(-2, 4)
23.
What is the axis of symmetry for the following equation?
y=4x2-8x+9
y=4x2-8x+9
a)
x=-8
b)
x=1
c)
1
d)
y=1
24.
What direction is the following equation opening?
y=-3x2-7x+8
y=-3x2-7x+8
a)
Up
b)
Down
c)
Left
d)
Right
25.
What is the vertex of y=x2+4x+3?
a)
(2,1)
b)
(-2,1)
c)
(0,0)
d)
(-2,-1)
26.
Find the Vertex:
f(x) = -2x2 + 4x -1
f(x) = -2x2 + 4x -1
a)
(1,1)
b)
(-2,4)
c)
(-1,-2)
d)
(0,-1)
27.
Find the Vertex:
y = x2 + 6x + 2
y = x2 + 6x + 2
a)
(-3,-7)
b)
(1,6)
c)
(6,2)
d)
(0,2)
28.
Find the Vertex:
h(x)= –3x2+12x+2
h(x)= –3x2+12x+2
a)
(2,14)
b)
(-3,12)
c)
(12,2)
d)
No Real Solution
29.
Does the following quadratic equation have a maximum or minimum value? How can you tell?
y=x²+2x-3
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
30.
What is the
y-intercept of: y=7x2+2x -1
y-intercept of: y=7x2+2x -1
a)
(0, 1)
b)
(0, -1)
c)
(1, 0)
d)
(-1, 0)
31.
What is the axis of symmetry of:
y=2x2–4x+9
y=2x2–4x+9
a)
x = 1
b)
x = -1
c)
x = -2
d)
x = 4
32.
Identify the 'a' value:
y = 16x2 -8x -24
y = 16x2 -8x -24
a)
16
b)
8
c)
-8
d)
-24
33.
What is the y-intercept of the following function
f(x) = -2x2 +3x - 7
f(x) = -2x2 +3x - 7
a)
(0, -2)
b)
(0, 3)
c)
(0, -7)
d)
(0, 7)
34.
Does the following function open up or down
y=–2x2 + 3x - 2
y=–2x2 + 3x - 2
a)
up
b)
down
35.
The vertex is...
a)
The highest point or the lowest point of the parabola
b)
The imaginary line that divides the parabola in half
c)
The initial value
d)
The point where the function crosses the x-axis
36.
A quadratic equation creates a...
a)
v-shaped graph
b)
a straight line
c)
a parabola
d)
a boomerang (L or J) shape
37.
What is the axis of symmetry for the following function
f(x) = 2x2 - 2x + 3
f(x) = 2x2 - 2x + 3
a)
x = 1/2
b)
y = 1/2
c)
x = 3
d)
y = 3
38.
The axis of symmetry line passes through which point?
a)
y-intercept
b)
x-intercept
c)
vertex
d)
none of these
39.
What is the formula to find the vertex of a parabola?
a)
x=b∕2a
b)
(o, c)
c)
x=−b∕2a
d)
x=−b∕a
40.
Find the y-intercept of
f(x) = 2x2 - 2x + 1
f(x) = 2x2 - 2x + 1
a)
(0,2)
b)
(0,-2)
c)
(0,1)
d)
(0,-1)
41.
Identify the vertex
a)
(-1,-9)
b)
(0,-8)
c)
(-4,0)
d)
x= -1
42.
Identify the y-intercept
a)
(-1,9)
b)
(0,-8)
c)
(-4,0)
d)
(2,0)
43.
Identify a root
a)
(-1,9)
b)
(0,-8)
c)
(-4,0)
d)
x= -1
44.
If a ball if thrown into the air is represented by the function
h(t) = -16t2+80t, where t represents the time in seconds and h(t) is the height of the ball in feet. Find the time it will take to reach its maximum height.
h(t) = -16t2+80t, where t represents the time in seconds and h(t) is the height of the ball in feet. Find the time it will take to reach its maximum height.
a)
8 mins
b)
2.5 seconds
c)
5 seconds
d)
604 seconds
45.
If a ball if thrown into the air is represented by the function
h(t) = -16t2+80t, where t represents the time in seconds and h(t) is the height of the ball in feet. Find the height of the ball at its maximum.
h(t) = -16t2+80t, where t represents the time in seconds and h(t) is the height of the ball in feet. Find the height of the ball at its maximum.
a)
240 ft
b)
160 ft
c)
300ft
d)
100ft
46.
What is the definition of an axis of symmetry?
a)
the line that cuts a quadratic in half
b)
place where the curve changes direction
c)
place where the curve crosses the x axis
d)
place where the curve crosses the y axis
47.
What direction is the following equation opening?
y=-3x2-7x+8
y=-3x2-7x+8
a)
Up
b)
Down
c)
Left
d)
Right
48.
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
49.
What is the axis of symmetry for the following equation?
y=4x2-8x+9
y=4x2-8x+9
a)
x=-8
b)
x=1
c)
x=-1
d)
x=2
50.
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
51.
Find the vertex of
f(x) = -x2 - 4x + 12
f(x) = -x2 - 4x + 12
a)
(-2, 16)
b)
(2, 0)
c)
(2, 4)
d)
(-2, 4)
52.
What is the axis of symmetry for the following equation?
y=2x2-8x+9
y=2x2-8x+9
a)
x= -4
b)
x= 2
c)
x= -2
d)
x= 4
53.
Find the vertex of the quadratic:
y = -2x2 + 4x + 3
y = -2x2 + 4x + 3
a)
(0, 3)
b)
(-1, -3)
c)
(1, 5)
d)
(-1, 1)
54.
What do we call the highest or lowest point of a quadratic?
a)
parabola
b)
vertex
c)
zero
d)
root
55.
Which equation below is a quadratic?
a)
y=9x+5
b)
y=3x2-6
c)
y=5x3+6
d)
x=3x
56.
What is the vertex of
y= x2 + 2x - 1 ?
y= x2 + 2x - 1 ?
a)
(-2, -9)
b)
(-1, -4)
c)
(1, 2)
d)
(-1, -2)
57.
In order to find the vertex, first find the x-coordinate using the equation _____ , and then find the y-coordinate by _____.
a)
x=−b∕2a ; plugging it into the equation
b)
x= b∕2a , plugging it into the equation
c)
x=−b∕2a , using (0,c)
d)
x= b∕2a , using (0,c)
58.
What is the y-intercept?
f(x) = -2x2 + 4x - 6
f(x) = -2x2 + 4x - 6
a)
(0, 6)
b)
(0, -6)
c)
(6, 0)
d)
(-6, 0)
59.
What are the x-intercepts of y = x2 - 3x - 10?
a)
(-3, 0) and (-10, 0)
b)
(-5, 0) and (2, 0)
c)
(5, 0) and (-2, 0)
d)
(5, 2)
60.
What is another word for zeros?
a)
y-intercepts
b)
roots
c)
vertex
d)
axis of symmetry
61.
What piece of information does c identify in the following equation?
y=ax2+bx+c
y=ax2+bx+c
a)
Zeroes
b)
Axis of Symmetry
c)
Direction
d)
y-intercept
62.
Suppose you have 54 feet of fencing to enclose a rectangular dog pen. The function
A = 27x − x 2 , where x = width
gives you the area of the dog pen in square feet. What width gives you the maximum area? What is the maximum area? Round to the nearest tenth as necessary.
A = 27x − x 2 , where x = width
gives you the area of the dog pen in square feet. What width gives you the maximum area? What is the maximum area? Round to the nearest tenth as necessary.
a)
width = 27 ft
area = 182.3 ft2
area = 182.3 ft2
b)
width = 27 ft
area = 391.5 ft2
area = 391.5 ft2
c)
width = 13.5 ft
area = 546.8 ft2
area = 546.8 ft2
d)
width = 13.5 ft
area = 182.3 ft2
area = 182.3 ft2
63.
Suppose that the equation
V = 20.8x2 – 458.3x + 3,500
represents the value of a car from 1964 to 2002, where x represents the number of years after 1964. In what year did the car have the least value?
V = 20.8x2 – 458.3x + 3,500
represents the value of a car from 1964 to 2002, where x represents the number of years after 1964. In what year did the car have the least value?
a)
1965
b)
1970
c)
1975
d)
1980
64.
The equation h = -16t2 + 32t models the height of a ball. Without a calculator, determine how many seconds it takes for the ball to reach its highest point.
a)
-2 seconds
b)
2 seconds
c)
0 seconds
d)
1 second
65.
The curve of the main suspension cables on a suspension bridge can be modeled by the function y=0.04x2 -x + 80 where y represents the height of the cable above the bridge surface and x represents distance along the bridge surface from one tower toward the other. How high are the towers?
a)
50 ft.
b)
80 ft.
c)
25 ft.
d)
Cannot be determined.
66.
The curve of the main suspension cables on a suspension bridge can be modeled by the function y=0.04x2 -x + 80 where y represents the height of the cable above the bridge surface and x represents distance along the bridge surface from one tower toward the other. How far along the bridge does the cable reach the closest point to the bridge?
a)
12.5 ft.
b)
73.75 ft.
c)
25 ft.
d)
Cannot be determined.
67.
The curve of the main suspension cables on a suspension bridge can be modeled by the function y=0.04x2 -x + 80 where y represents the height of the cable above the bridge surface and x represents distance along the bridge surface from one tower toward the other. What is the closest the cable comes to the bridge surface?
a)
12.5 ft.
b)
73.75 ft.
c)
25 ft.
d)
Cannot be determined.
68.
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
69.
What is the domain of the function? (the domain is the set of x-values used)
a)
x≥3
b)
x≤3
c)
All real numbers
d)
-1≤x≤5
70.
What is the range of the function? (the range is the set of y-values used)
a)
y≤3
b)
y≥3
c)
All real numbers
d)
-6≤y≤3
71.
On what interval is the function shown increasing?
a)
x < -3
b)
x > -3
c)
x < -2
d)
x > -2
72.
What is the point on the graph where the y-coordinate is zero?
a)
Y-Axis
b)
X-Axis
c)
Y-Intercept
d)
X-Intercept
73.
What is the point on the graph where the x-coordinate is zero?
a)
X- Intercept
b)
X-Axis
c)
Y-Intercept
d)
Y-Axis
74.
What is the y-intercept of the equation
y = x2+8
y = x2+8
a)
(0,3)
b)
(3,0)
c)
(0,8)
d)
Doesn't have one
75.
What is the y-intercept of the equation
y = 2x2
y = 2x2
a)
(0,2)
b)
(0,0)
c)
(0,8)
d)
Doesn't have one
76.
Where is the AoS (Axis of Symmetry) for
y = 0.5x2+4x+2
y = 0.5x2+4x+2
a)
x = 0
b)
x = 1
c)
x = -1
d)
x = -4
77.
Where is the AoS (Axis of Symmetry) for
y = 4x2+4
y = 4x2+4
a)
x = 0
b)
x = 1
c)
x = -1
d)
x = 4
78.
Which function has a y-intercept of (0,4)
a)
y = x2 + 4x
b)
y = x2 + 4
c)
y = x2 - 4x
d)
y = x2 - 4
79.
Which function has x-intercepts at 0 and -4
a)
y = x2 + 4x
b)
y = x2 + 4
c)
y = x2 - 4x
d)
y = x2 - 4
80.
Which function has an Axis of Symmetry at
x = 2
x = 2
a)
y = x2 + 4x
b)
y = x2 + 4
c)
y = x2 - 4x
d)
y = x2 - 4
81.
Which function has zeros at 2 and -2
a)
y = x2 + 4x
b)
y = x2 + 4
c)
y = x2 - 4x
d)
y = x2 - 4
82.
What is the vertex of the function
y = x2 - 2x
y = x2 - 2x
a)
(1, -2)
b)
(1, -1)
c)
(-2, 1)
d)
(0, 0)
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