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Key Features of Quadratic Functions

Total questions: 55

Worksheet time: 1hrs 17mins

Name
Class
Date
1.

Define X-intercept

a)

The highest or lowest point on the graph

b)

Where the parabola touches or intersects the x-axis

c)

Where the parabola touches or intersects the y-axis

d)

A line that divides the graph into two equal parts. i.e. cuts the graph in half

2.

Define Y-intercept

a)

Where the parabola touches or intersects the x-axis, also called the x-intercept

b)

The lowest y-value on the graph

c)

The highest y-value on the graph

d)

Where the parabola touches or intersects the y-axis

3.

Define Zero

a)

Where the parabola touches or intersects the x- axis, also called the x-intercept

b)

A line that divides the graph into two equal parts. i.e. cuts the graph in half

c)

The highest or lowest point on the graph

d)

Where the parabola touches or intersects the y-axis

4.

Define Maximum

a)

The highest or lowest point on the graph

b)

The highest y-value on the graph

c)

The lowest y-value on the graph

d)

A line that divides the graph into two equal parts. i.e. cuts the graph in half

5.

Define Minimum

a)

The highest y-value on the graph

b)

Where the parabola touches or intersects the y-axis

c)

Where the parabola touches or intersects the x-axis, also called the x-intercept

d)

The lowest y-value on the graph

6.

Define Vertex

a)

Where the parabola touches or intersects the x-axis

b)

The highest or lowest point on the graph

c)

Where parabola line touches or intersects the x- axis, also called the x-intercept

d)

A line that divides the graph into two equal parts. i.e. cuts the graph in half

7.

Define Axis Of Symmetry

a)

A line that divides the graph into two equal parts. i.e. cuts the graph in half

b)

Where the parabola touches or intersects the x-axis, also called the x-intercept

c)

The highest y-value on the graph

d)

The highest or lowest point on the graph

8.

Define Roots

a)

Where the parabola touches or intersects the y-axis

b)

The lowest y-value on the graph

c)

Where the parabola touches or intersects the x-axis, also called the x-intercept

d)

A line that divides the graph into two equal parts. i.e. cuts the graph in half

9.

Define Solution

a)

The highest y-value on the graph

b)

Where the parabola touches or intersects the y-axis

c)

The highest or lowest point on the graph

d)

Where the parabola touches or intersects the x-axis, also called the x-intercept

10.

Define Roots, Zeros, X-intercept, and Solutions

a)

Where the parabola touches or interests the x-axis

b)

Where the parabola touches or interests the y-axis

11.
What is the vertex of the graph?
a)
(2, 4)
b)
(3, -1)
c)
(0, 8)
d)
(4, 2)
12.
Is this a max or min?
a)
max
b)
min
13.

Find the increasing interval

a)

x<2

b)

x<0

c)

x>2

d)

x>-2

14.

Find the decreasing interval

a)

x>-2

b)

x<-2

c)

x>2

d)

x<2

15.

Find the increasing interval

a)

x>-1

b)

x<-1

c)

x<4

d)

x>-4

16.

Find the decreasing interval

a)

x>-1

b)

x<-1

c)

x>4

d)

x<4

17.

Identify the y-intercept

a)

(0, -3)

b)

(3, 0)

c)

(0, 3)

d)

(2, 1)

18.

What is the end behavior?

a)

The end behavior of the graph is x →∞, f(x)→⁻∞ and x →⁻∞,f(x)→⁻∞

b)

The end behavior of the graph is x →∞, f(x)→∞ and x→⁻∞, f(x)→∞

c)

The end behavior of the graph is x →∞, f(x)→∞ and x→⁻∞, f(x)→0

d)

The end behavior of the graph is x →∞,f(x)→∞ and x→⁻∞, f(x)→⁻∞

19.
Name the x-intercept(s)?
a)
(0, 0)
b)
(2, 4)
c)
(0, 0) and (0, 4)
d)
(0, 0) and (4, 0)
20.
Does this graph in the back have maximum or minimum value?
a)
maximum
b)
minimum
c)
neither
d)
both
21.
.How many zeros does this parabola have? 
a)
3
b)
2
c)
0
d)
1
22.
Is this point a max or min?
a)
max
b)
min
23.
The graph of a quadratic function is shown.
What statement about this graph is not true?
a)
The graph has a y-intercept at (0, 8)
b)
The graph has a maximum point at (-1, 9)
c)
The graph has an x-intercept at (2, 0)
d)
The graph has the y-axis as a line of symmetry
24.

What is the range of the function shown?

a)

y < -1

b)

y > -1

c)

y ≥ -1

d)

y ≤ -1

25.

Which of the following are true about the quadratic function shown? (You can choose more than one answer)

a)

There are two roots

b)

the axis of symmetry is at x = -2

c)

the vertex is a maximum

d)

the vertex is (-2, 0)

26.

Which of the following quadratics has a range of all real numbers less than or equal to 4?

a)
b)
c)
d)
27.

Determine the domain and range of the function

a)

Domain: All real numbers, Range: All real numbers

b)

Domain: x ≥ -4, Range: All real numbers

c)

Domain: All real numbers, Range: y ≥ -4

d)

Domain: -1 ≤ x ≤ 5, Range: y ≥ -4

28.

Which function has a domain of all real numbers?

a)
b)
c)
d)

All of the above

29.

Which function has an axis of symmetry of x = 0?

a)
b)
c)
d)

None of the above

30.

Which function has an x-intercept and y-intercept at (0, 0)?

a)
b)
c)
d)
31.
About how long did it take the football to hit the ground (0 feet)?
a)
About 3 seconds
b)
About 0 seconds
c)
About 1.3 Seconds
d)
About 2.6 Seconds
32.
Members of the math club launch a model rocket from ground level with an initial velocity of 96 ft/sec.  This can be modeled with the function h(t) = -16t2 + 96t.  What is the maximum height?
a)
145 feet
b)
160 feet
c)
130 feet
d)
135 feet
33.
What is the axis of symmetry for the given table?
a)
x = 6
b)
x = 0
c)
x = 1
d)
x = ½
34.

Which is an x-intercept of the table?

a)

(1, -6)

b)

(-2, 0)

c)

(0, -6)

d)

(3, 0)

35.

Which is a y-intercept of the table?

a)

(1, -6)

b)

(-2, 0)

c)

(0, -6)

d)

(3, 0)

36.

Which approximates the vertex?

a)

(1, -6)

b)

(-2, 0)

c)

(0.5, -7)

d)

(3, 0)

37.
A ball is tossed in the air from a height of 5 feet and the following data is recorded. What is the x-intercept?
a)
(0, 5) 
b)
(0.5, 9)
c)
(1.25, 0)
d)
(1.0, 5)
38.

What is the vertex of the following equation?


f(x) = x2 - 6x + 13

a)

(6, 3)

b)

(0, 13)

c)

(2, 8)

d)

(3, 4)

39.

What is the y-intercept of the following equation?


f(x) = 3x2 + 2x - 5

a)

(3, 0)

b)

(0, -5)

c)

(2, 1)

d)

(0, 3)

40.

Does the following equation have a maximum or a minimum?


f(x) = -3x2 +2x + 5?

a)

Maximum

b)

Minimum

41.

Does the following equation have a maximum or minimum?


f(x) = 4x2 - 5x + 3

a)

Maximum

b)

Minimum

42.

What is the vertex of the following equation?


f(x) = 4x2 - 8x - 6

a)

(1, -10)

b)

(1, 0)

c)

(10, 0)

d)

(-5, 2)

43.
Which one of the following best describes the point (0, -28) on the function below
f(x) = x2 +3x - 28?
a)
(0, - 28) is the y-intercept
b)
(0, - 28) is the zero
c)
(0, - 28) is the solution
d)
(0, - 28) is the maximum vertex
44.

Which of the following statements about the following equations is FALSE?


f(x) = x2 + 8x +7

a)

The vertex is (-4, -9)

b)

The axis of symmetry is x = -4

c)

The roots are (-7, 0) and (-1, 0)

d)

The y-intercept is (0, -3)

45.
The graph of a quadratic function is called a
a)
Parabola
b)
Vertex
c)
Axis of Symmetry 
d)
Vertex Form
46.

What is the domain and range of the following function:

y = 3x² -6x +5

a)

Domain: all real numbers

Range: all numbers less than or equal to 2

b)

Domain: all real numbers

Range: all numbers greater than 2

c)

Domain: all real numbers

Range: all numbers greater than or equal to 2

d)

Domain: all real numbers

Range: all numbers less than 2

47.
Which quadratic function is represented by 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
48.
What is the domain and range of the following function:
y = 3x2 - 54x + 241
a)
Domain: (-∞, ∞)
Range: [-2, ∞)
b)
Domain: (-∞, ∞)
Range: (-∞, -2]
c)
Domain: (-∞, ∞)
Range: [9, ∞)
d)
Domain: (-∞, ∞)
Range: (-∞, 9]
49.
What is the domain and range of the following function:
y = x2 - 18x + 86
a)
Domain: (-∞, ∞)
Range: [9, ∞)
b)
Domain: (-∞, ∞)
Range: [5, ∞)
c)
Domain: (-∞, ∞)
Range: (-∞, 9]
d)
Domain: (-∞, ∞)
Range: (-∞, 5]
50.

f(x) = x2-12x+35

What are the intervals of increasing and decreasing for this function?

a)

Increasing: x > 6

b)

Decreasing: x > 6

c)

Increasing: x < 6

d)

Decreasing: x < 6

51.

y = 3x2 - 5x + 2

What are the end behaviors for this function?

a)

As x gets bigger, y gets bigger.

b)

As x gets bigger, y gets smaller.

c)

As x gets smaller, y gets bigger.

d)

As x gets smaller, y gets smaller.

52.

f(x) = -x2-4x-7

What are the intervals of increasing and decreasing for this function?

a)

Increasing: x > -2

b)

Decreasing: x > -2

c)

Increasing: x < -2

d)

Decreasing: x < -2

53.

y = -5x2 +23x -32

What are the end behaviors for this function?

a)

x → ⁻∞, y → ⁻∞ and x → ⁻∞, y → ⁻∞

b)

x → ∞, y → ⁻∞ and x → ⁻∞, y → ⁻∞

c)

x → ∞, y → ∞ and x → ⁻∞, y → ∞

d)

x → ∞, y → ∞ and x → ∞, y → ∞

54.
What is the end behavior for
f(x)=2x2+x
a)
A
b)
B
c)
C
d)
D
55.
Describe the end behavior of the graph.
a)
x →∞, y→⁻∞ and x →⁻∞,y→⁻∞
b)
x →∞, y→∞ and x→⁻∞, y→∞
c)
x →∞, y→∞ and x→⁻∞, y→0
d)
x →∞,y→∞ and x→⁻∞, y→⁻∞

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