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Worksheets

Quadratic Functions and Graphs

Total questions: 42

Worksheet time: 29mins

Name
Class
Date
1.

1. The graph of a quadratic function is shown below: Find the following key features about the quadratic function: The vertex is: ______ The equation of axis of symmetry is: ______ The vertex is at a ______ (maximum or minimum) value of ______

a)

The vertex: (-2, -1), The equation of axis of symmetry is: x =- 2, The vertex is at a minimum value of -11

b)

The vertex: (-1, -4), The equation of axis of symmetry is: x = -1, The vertex is at a maximum value of -4

c)

The vertex: (0, 0), The equation of axis of symmetry is: x = 0, The vertex is at a minimum value of 0

d)

The vertex: (3, 2), The equation of axis of symmetry is: x = 3, The vertex is at a maximum value of 2

2.

The graph of a quadratic function is shown below: Which statement is true based on the given graph?

a)

The function has a zero at -8.

b)

The maximum value of the function is -4.

c)

The equation of the axis of symmetry of the graph is x=-4

d)

The vertex of the graph is (-4,-2).

3.

The graph of a quadratic function is shown below. What are the zeros of the function? Select TWO correct points that represent the solutions.

a)

(2,0)

b)

(3,-1)

c)

(6,8)

d)

(4,0)

e)

(0,8)

4.

The table represents some points on the graph of a quadratic function, f. Find the range of f.

a)

All real numbers greater than or equal to 2.

b)

All real numbers less than or equal to 2.

c)

All real numbers greater than -19/4

d)

All real numbers less than or equal to -19/4

5.

Function f is defined by f(x) = 2x2+3x=52x^2 + 3x = 5 . What are the solutions to the function?

a)

x=-1 and x= -5/2

b)

x=1 and x= 2/5

c)

x=1 and x= -5/2

d)

x=-1 and x= 2/5

6.

What are the solutions to the equation x22x=19x^2 - 2x = 19 ?

a)

x = -1 ± √20

b)

x = 1 ± √20

c)

x = -2 ± √2

d)

x = 5 ± √2

7.

Find the positive solution of x26x=40x^2 - 6x = 40 ?

a)

x=6

b)

x=10

c)

x=8

d)

x=-4

8.

If f(x) = x2x^2 was transformed to create the function g(x) = f(x - 2) - 3, find the vertex. (_____,_____)

a)

(2,-3)

b)

(0,0)

c)

(-2,3)

d)

(3,-2)

9.

The quadratic function h, h(12) = 0 and h(−5/2) = 0. What is a possible equation for h in factored form? HINT: ORDER MATTERS HERE!!!!

(a)  

10.

An experiment examines the relationship between the number of miles a car travels per gallon of gasoline and the speed of the car, x, in miles per hour.

Which function best models the data? (Round to 2 decimal places)

a)

f(x) = 0.02x² − 1.13x + 46.65

b)

f(x) = 0.08x² − 0.10x + 45

c)

f(x) = −0.08x² − 0.10x + 45

11.

The graph of the function g is shown below. Which function is best represented by the graph?

a)

g(x) = x² − 2x − 8

b)

g(x) = −x² − 2x − 8

c)

g(x) = −x² + 2x + 8

d)

g(x) = x² + 2x − 8

12.

The quadratic function f(x) = x² is transformed to create g shown below. What is the equation of g?

a)

g(x) = f(x − 2) + 1

b)

g(x) = 3f(x + 2) + 1

c)

g(x) = 3f(x − 2) + 1

d)

g(x) = f(x + 2) − 1

13.

If the quadratic parent function f(x)= x^2 to create g(x)= f(x-1)-3. The graph of f is translated ______ by 1 unit and ______ by 3 units to create the graph of function of g.

a)

left, down

b)

right, up

c)

left, up

d)

right, down

14.

Which quadratic function in vertex form can be represented by the graph that has a vertex at (2,10) and passes through the point (4,22)?

a)

y = 2(x − 2)² + 10

b)

y = 3(x − 2)² + 10

c)

y = 2(x + 3)² − 6

d)

y = 3(x − 3)² + 6

15.

Find the domain of f(x) = −x² − 10x.

a)

All real numbers

b)

All real numbers greater than or equal to 25

c)

All real numbers less than or equal to 25

d)

All real numbers greater than or equal to 0 and less than or equal to 25

16.

If f(x) = x² was reflected and shifted left 3 units and down 4 units to create g, which quadratic function represents the new graph of g?

a)

f(x) = −(x + 4)² − 3

b)

f(x) = −(x + 3)² − 4

c)

f(x) = (x + 3)²

d)

f(x) = −(x − 4)²

17.

How old is Ms. Cerda?

(a)  

18.

Ms. Cap is a millennial.

a)
True
b)
False
19.

Ms. Cerda graduated from Wunsche HS in 2022.

a)
True
b)
False
20.

What is Ms. Cap’s favorite football team?

a)

Steelers

b)

Texans

c)

Bills

d)

Cowboys

21.

What college does Ms. Cerda attend?

a)

University of Houston

b)

Sam Houston State University

c)

Texas Tech University

d)

University of Houston-Downtown

22.

Domain is….

a)

x

b)

y

23.

Range is…

a)

x

b)

y

24.

What is another word for solutions? (Select TWO answers)

a)

x-interecepts

b)

y-intercepts

c)

zeros

25.

Ms. Cap has 3 dogs.

a)
True
b)
False
26.

Who is taller?

a)

Ms. Cap

b)

Ms.Cerda

27.

What does G.O.A.T stand for?

a)

goat of all time

b)

greatest of all time

c)

greatest of all teachers

d)

gifted overachiever and thinker

28.

f(x) is a fancy way of saying….

a)

x

b)

y

29.

This is a baby picture of Ms. Cap

a)
True
b)
False
30.

Who is this baby?

a)

Ms. Cerda

b)

Ms. Cap

c)

AI Generated

d)

Google Photo

31.

Ms. Cap’s natural hair color is blonde

a)
True
b)
False
32.

Ms. Cap has been teaching for 13 years.

a)
True
b)
False
33.

This is a picture of Ms. Cerda.

a)

True

b)

False

34.

What is Ms. Cerda’s dog’s name?

a)

Clutch

b)

El Chavo

c)

Max

d)

Bob

35.

Where is this cat from?

a)

Ms. Cerda

b)

Ms. Cap

c)

AI generated

d)

Instagram

36.

This cat is AI generated.

a)
True
b)
False
37.

Find the domain of the graph.

a)

All real numbers.

b)

All real numbers greater than or equal to -3.

c)

All real numbers less than or equal to -3.

d)

All real numbers greater than or equal to 0.

38.

Find the range of the graph.

a)

All real numbers.

b)

All real numbers greater than or equal to -3.

c)

All real numbers less than or equal to -3.

d)

All real numbers less than 0.

39.

The red graph shifted where?

a)

down by 2

b)

up by 1

c)

down by 1

d)

up by 2

40.

The RED graph shifted where?

a)

left by 1

b)

right by 1

c)

down by 1

d)

up by 1

41.

How many solutions does the graph have?

a)

1

b)

none

c)

2

42.

What is the y-intercept on the graph?

a)

(0,-3)

b)

(-3,0

c)

(0,0)

d)

(0,3)