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Modeling with Quadratic Functions - Printable Math Worksheets 10th Grade - Wayground

Modeling with Quadratic Functions

Anthony Clark

Created by Anthony Clark

20 questions

10th Grade

Math

Updated Feb 2026

This Grade 10 mathematics worksheet gives students 20 multiple-choice questions on modeling real-world situations with quadratic functions. Students evaluate quadratic equations for a given time, identify the vertex as the maximum height, determine when an object reaches that height, and interpret x- and y-intercepts in projectile and vertical-motion contexts. Several questions also ask students to choose the quadratic equation that best models data presented in tables or graphs, including projectile, text-message, and other modeled situations. The practice connects algebraic features of a quadratic function to their meaning in context: maximum height, time in the air, initial height, and the moment an object reaches the ground. Students work with examples involving rockets, soccer balls, divers, and rocks launched from cliffs, reinforcing how to read and use quadratic models rather than only manipulate equations symbolically. This free printable worksheet includes a complete answer key for classroom practice, independent work, or review.

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Modeling with Quadratic Functions

Total questions: 20

Name
Class
Date
1.
The height of an object thrown into the air can be modeled by the formula h(t) = -16t 2 + 70t + 95, where h(t) is in feet…

The height of an object thrown into the air can be modeled by the formula h(t) = -16t2 + 70t + 95, where h(t) is in feet after t seconds.
What is the height of the object after 5 seconds?

a)

95 feet

b)

45 feet

c)

70 feet

d)

171.56 feet

2.

The equation h(t)=−16t2+350t+40h\left(t\right)=-16t^2+350t+40 models the position of a rocket that was launched into the air. How do you find the time it will take for the rocket to reach maximum height?

a)

Calculate the time using: t=−b2at=-\frac{b}{2a}

b)

Plug the answer you get for the time into h(t)=−16t2+350t+40h\left(t\right)=-16t^2+350t+40 to get the maximum height

c)

Look for the maximum height given in the original equation

d)

Find both coordinates of the vertex

3.

The quadratic function shown below is used to model vertical motion. h(t)=−16t2+vot+hoh\left(t\right)=-16t^2+v_ot+h_o If a soccer ball is kicked upward from ground level with an initial velocity of 64 ft/s, how long will it take to get to its maximum height?

a)

t = 3 seconds

b)

t = 10 second

c)

t = 4 seconds

d)

t = 2 seconds

4.

When the question says, "What is the maximum height the ball reaches?", what are you looking for on the graph?

a)

vertex

b)

x-intercept

c)

y-intercept

d)

point on the graph

5.
Q32

Q32

a)

y = 0.001x2 - 0.426x + 35.672

b)

y = -0.60x2 + 348.1x - 334.2

c)

y = 0.001x2 + 35.672

d)

y = -0.60x2 - 334.2

6.
A company collected data for the number of text messages sent and received using a text-message application since October…

A company collected data for the number of text messages sent and received using a text-message application since October 2011. The table shows the number of text messages sent and received in billions over time. The data can be modeled by a quadratic function. Which function best models the data?

a)

n(t)=−0.002t2 +0.55t+5.02n\left(t\right)=-0.002t^2\ +0.55t+5.02

b)


n(t)=0.072t2−0.15t+2.73n\left(t\right)=0.072t^2-0.15t+2.73

c)

n(t)=−0.002t2 +5.02n\left(t\right)=-0.002t^2\ +5.02

d)

n(t)=0.072t2+2.73n\left(t\right)=0.072t^2+2.73

7.
Question Image
a)
b)
c)
d)
8.
Question Image

a)

A

b)

B

c)

C

d)

D

9.
Question Image
a)

A

b)

B

c)

C

d)

D

10.
A projectile is launched into the air from the ground. The table shows the height of the projectile, , at different times.…

A projectile is launched into the air from the ground. The table shows the height of the projectile, h(t)h\left(t\right) , at different times.

Based on the table, which function can be used to model this situation?

a)

h(t)=99t2+858h\left(t\right)=99t^2+858

b)

h(t)=−4.9t2+295t+0.6h\left(t\right)=-4.9t^2+295t+0.6

c)

h(t)=−4.9t2+295t+2h\left(t\right)=-4.9t^2+295t+2

d)

h(t)=99t2+1,470.3h\left(t\right)=99t^2+1,470.3

11.
A company collected data for the number of text messages sent and received using a text-message application since October…

A company collected data for the number of text messages sent and received using a text-message application since October 2011. The table shows the number of text messages sent and received in billions over time. The data can be modeled by a quadratic function. Which function best models the data?

a)

n(t)=−0.002t2 +0.55t+5.02n\left(t\right)=-0.002t^2\ +0.55t+5.02

b)


n(t)=0.072t2−0.15t+2.73n\left(t\right)=0.072t^2-0.15t+2.73

c)

n(t)=−0.002t2 +5.02n\left(t\right)=-0.002t^2\ +5.02

d)

n(t)=0.072t2+2.73n\left(t\right)=0.072t^2+2.73

12.
Which function best models the data?

Which function best models the data?

a)

y=−1.51x2+283.75x−16.23y=-1.51x^2+283.75x-16.23

b)

y=−16.23x2+283.75x−1.51y=-16.23x^2+283.75x-1.51

c)

y=−1.51x2+16.23x−283.75y=-1.51x^2+16.23x-283.75

d)

y=16.23x2+283.75x−1.51y=16.23x^2+283.75x-1.51

13.
TEK A.8 (B)

TEK A.8 (B)

a)

d(x) = 0.05x2 + 0.74x

b)

d(x) = 0.05x2 + 0.74x + 9.17

c)

d(x) = 0.26x2 – 3.11x

d)

d(x) = 0.26x2 – 3.11x + 1

14.
Question Image
a)

A

b)

B

c)

C

d)

D

15.
TEK A.8 (B)

TEK A.8 (B)

a)

d(x) = 0.05x2 + 0.74x

b)

d(x) = 0.05x2 + 0.74x + 9.17

c)

d(x) = 0.26x2 – 3.11x

d)

d(x) = 0.26x2 – 3.11x + 1

16.

The quadratic function shown below is used to model the vertical motion of a soccer ball being kicked from the ground level: h(t)=−16t2+64th\left(t\right)=-16t^2+64t . How high will it go? 

a)

100 feet

b)

64 feet

c)

140 feet

d)

88 feet

17.

A diver is standing on a platform above the pool. He jumps form the platform with an initial upward velocity of 8 ft/s. Use the formula: h(t) = −16 t2 + 8t + 24

How high is the platform?

a)

.25 ft

b)

24 ft

c)

25 ft

d)

8 ft

18.
A kid launches a rock off of a cliff. The height of the rock after t seconds can be modeled by the graph shown. What is the…

A kid launches a rock off of a cliff. The height of the rock after t seconds can be modeled by the graph shown. What is the height of the cliff?

a)

1.094 ft

b)

174.141 ft

c)

155 ft

d)

4.393 ft

e)

None of the above

19.
A kid launches a rock off of a cliff. The height of the rock after t seconds can be modeled by the graph shown. When does…

A kid launches a rock off of a cliff. The height of the rock after t seconds can be modeled by the graph shown. When does the rock hit the ground?

a)

1.094 seconds

b)

174.141 seconds

c)

155 seconds

d)

4.393 seconds

e)

None of the above

20.
A kid launches a rock off of a cliff. The height of the rock after t seconds can be modeled by the graph shown. What is the…

A kid launches a rock off of a cliff. The height of the rock after t seconds can be modeled by the graph shown. What is the maximum height the rock reaches ?

a)

1.094 ft

b)

174.141 ft

c)

155 ft

d)

4.393 ft

e)

None of the above

WaygroundAnswer Key

Modeling with Quadratic Functions

Total questions: 20

1.
b)

45 feet

2.
a)

Calculate the time using: t=−b2at=-\frac{b}{2a}

3.
d)

t = 2 seconds

4.
a)

vertex

5.
b)

y = -0.60x2 + 348.1x - 334.2

6.
b)


n(t)=0.072t2−0.15t+2.73n\left(t\right)=0.072t^2-0.15t+2.73

7.
b)
8.
b)

B

9.
b)

B

10.
b)

h(t)=−4.9t2+295t+0.6h\left(t\right)=-4.9t^2+295t+0.6

11.
b)


n(t)=0.072t2−0.15t+2.73n\left(t\right)=0.072t^2-0.15t+2.73

12.
b)

y=−16.23x2+283.75x−1.51y=-16.23x^2+283.75x-1.51

13.
c)

d(x) = 0.26x2 – 3.11x

14.
a)

A

15.
c)

d(x) = 0.26x2 – 3.11x

16.
b)

64 feet

17.
b)

24 ft

18.
c)

155 ft

19.
d)

4.393 seconds

20.
b)

174.141 ft

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FAQs

What does the Modeling with Quadratic Functions worksheet cover?

This Grade 10 worksheet uses 20 multiple-choice questions to build skill in interpreting quadratic functions as real-world models. Students substitute values into height equations, identify the vertex to find maximum height, use the vertex’s time coordinate to determine when an object peaks, interpret intercepts for initial height and ground contact, and select equations that fit tables or graphs.

How can I use this worksheet to teach modeling with quadratic functions?

Introduce the worksheet by connecting each feature of a vertical-motion quadratic to its meaning: the vertex represents maximum height, the y-intercept represents the starting height, and an x-intercept can represent when the object reaches the ground. Model one substitution question, then have students explain why a maximum-height question requires the vertex rather than an intercept. As students complete the equation-selection items, ask them to compare the signs, terms, and data patterns before choosing a model.

What mistakes should I watch for when students complete this worksheet?

Watch for students substituting the given time incorrectly into a height equation or reporting the maximum height when the question asks for the time to reach it. Students may also confuse the vertex with an x- or y-intercept, treating the initial height as the ground-contact time or vice versa. In the table- and graph-based modeling questions, check that they do not choose an equation simply because some coefficients look familiar; the selected function must match the data and context.

How do I assign and grade this quadratic-functions worksheet?

Wayground provides this worksheet as a printable PDF and as a digital quiz, so you can choose paper-based or online practice for the 20 multiple-choice questions. It includes a complete answer key, and printable submissions can be graded by scanning student work with the Wayground for Teachers app. The printable format can also support schools that are reducing screen time.

How can I differentiate this worksheet for my students?

Use the worksheet’s Advanced Settings to adjust font spacing and font size so the quadratic equations, answer choices, and graph- or table-based prompts are easier to read. You can also apply a dyslexia-friendly font or translate the worksheet into another language while keeping the multiple-choice format and quadratic-modeling practice intact.

Where can I find more worksheets like this on Wayground?

Wayground offers a broad collection of free printable worksheets and practice problems across subjects, with downloadable PDFs and answer keys to help students master essential skills and concepts. Browse more resources at https://wayground.com/en-us/worksheets.

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