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Quadratic Word Problems - Printable Mathematics Worksheets - Wayground

Quadratic Word Problems

15 questions

9th - 9th Grade

Mathematics

Quadratic Word Problems is a Grade 9 mathematics worksheet with 15 multiple-choice questions that apply quadratic equations to real-world height and motion situations. Students evaluate height at a given time, determine an object’s maximum height, find when it reaches that maximum, calculate when it returns to the ground or water, and identify an initial height from a model. The problems use contexts such as thrown toys, fireworks, jumping animals, golf balls, rockets, and falling objects, helping students connect the coefficients and outputs of a quadratic function to time and height. This free printable worksheet is useful for guided practice, independent work, homework, or a formative check after instruction on quadratic models. It includes a complete answer key so teachers can review students’ equation-based reasoning and identify which interpretation skills need reinforcement.

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Quadratic Word Problems

Total questions: 15

Name
Class
Date
1.

An object in launched directly upward at 64 feet per second (ft/s) from a platform 80 feet high. Its height is represented by the equation

s(t) = –16t2 + 64t + 80

What will be the object's maximum height?

a)

2 ft

b)

80 ft

c)

144 ft

d)

64 ft

2.

A frog is sitting on the ground when he is scared by a big dog. His movement is modeled by the equation h = -6t2 + 6t where h is the frog's height at any given time, t . How many seconds until the frog is back on the ground?

a)

0.5 seconds

b)

1 second

c)

1.5 seconds

d)

2 seconds

e)

3 seconds

3.

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

4.

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

5.

A lizard is jumping across the water in search of food. The equation h = -12t2 + 6t models the lizard's height in feet above the water t seconds after he jumps. How long after jumping is he back on the water?

a)

0.1 seconds

b)

0.25 seconds

c)

0.50 seconds

d)

0.75 seconds

e)

1 second

6.

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

7.

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

8.

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

9.

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

10.

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

11.

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

12.
A diver is standing on a platform above the pool. He jumps form the platform with an initi8al upward velocity of 8 ft/s. Use the formula h t = −16 t2 + 8t + 24, where h is his height above the water, t is the time, v is his starting upward velocity, and s is his starting height. How high is the platform?
a)
.25 ft
b)
24 ft
c)
25 ft
d)
8 ft
13.

The function f(t) = -5t2+20t + 60 models the approximate height of an object t seconds after it is launched. How many seconds does it take the object to hit the ground?

a)

4 seconds

b)

2 seconds

c)

6 seconds

d)

9 seconds

14.

You jump off a 24 foot high cliff and your fall is modeled by the function:

h(t) = -16t2 + 8t + 24

How long would it take you to hit the water?

a)

8 seconds

b)

1 second

c)

1.5 seconds

d)

1/4 second

15.

Rafael drops a ball from a third-story window. This equation represents the approximate height, h, in meters, of the ball above the ground after it falls for t seconds.

h = -5t2 + 45

When is the ball at ground level?

a)

only at t = 0 seconds

b)

only at t = 3 seconds

c)

only at t = 9 seconds

d)

at both t = 0 seconds and t = 3 seconds

Answer Key

Quadratic Word Problems

Total questions: 15

1.
c)

144 ft

2.
b)

1 second

3.
d)

8 feet

4.
b)

0.25 seconds

5.
c)

0.50 seconds

6.
c)

9

7.
e)

210.25

8.
b)

2.25 seconds

9.
d)

9

10.
c)

1.5

11.
c)

48

12.
b) 24 ft
13.
c)

6 seconds

14.
c)

1.5 seconds

15.
b)

only at t = 3 seconds

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FAQs

What does the Quadratic Word Problems worksheet cover?

This Grade 9 worksheet uses 15 multiple-choice word problems to practice interpreting quadratic equations that model height over time. Students find values such as height at a specified time, maximum height, time at maximum height, and when an object reaches the ground or water.

How can I use this worksheet to teach quadratic height-and-motion problems?

Introduce the worksheet by having students identify what each equation represents: the coefficient of the squared term, the time variable, and the starting height. Then model how to choose the appropriate strategy—substituting a time value, finding the vertex for a maximum, or solving for height zero—before students complete the multiple-choice items and explain why their selected answer fits the situation.

What mistakes should I watch for when students complete these quadratic word problems?

Students may substitute the wrong time value, confuse a maximum height with the time needed to reach it, or ignore the constant term that represents the starting height. In questions about hitting the ground or returning to the water, check that students interpret the relevant nonnegative time rather than selecting a mathematically possible but physically inappropriate value.

How do I assign and grade this Quadratic Word Problems worksheet?

The worksheet is available as a printable PDF and as a digital quiz on Wayground, and it includes a complete answer key for all 15 multiple-choice questions. Printable submissions can be graded by scanning student work with the Wayground for Teachers app.

How can I differentiate this quadratic word-problem worksheet for my students?

Use the worksheet’s Advanced Settings to adjust font spacing or increase the font size so the quadratic equations and answer choices are easier to read. You can also apply a dyslexia-friendly font or translate the multiple-choice word problems into another language when that better supports access to the height-and-motion contexts.

Where can I find more free worksheets like this on Wayground?

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

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