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Grade 9 · Math · Algebra 1

9th grade Quadratic word problems, and choosing a method worksheet

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Quadratic word problems, and choosing a method

Grade 9 Math Worksheet - Challenge Me

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Circle the best answer, or write your answer on the line.

  1. Esme tosses a striped play ball up at 56 feet per second from the ground: h = -16t² + 56t. When is it 40 feet high for the first time, in seconds?

  2. Jun kicks a soccer ball up at 64 feet per second: h = -16t² + 64t. When is it 48 feet high for the second time, in seconds?

  3. Kira launches a toy foam rocket at 80 feet per second: h = -16t² + 80t. When is it 64 feet high for the first time, in seconds?

  4. Luz tosses a basketball up at 72 feet per second: h = -16t² + 72t. When is it 56 feet high for the second time, in seconds?

  5. Pia's garden is 10 by 6 meters, with a path x meters wide all around. Garden and path cover 96 square meters. How wide is x?

  6. Ren's 16 by 10 foot rug has an even strip of bare floor x feet wide all around it. Rug and strip cover 280 square feet. How wide is x?

  7. Zee times a play ball a presenter drops from a 25 m tower into a net: h = -4.9t² + 25. To the nearest tenth, after how many seconds does it land?

  8. In a science video Ari watches, a pebble drops from a 45 m bridge into a river: h = -4.9t² + 45. To the nearest tenth, after how many seconds does it land?

  9. Bo times a water balloon a teacher drops from a 30 m tower onto grass: h = -4.9t² + 30. To the nearest tenth, after how many seconds does it land?

  10. For an egg-drop project, Esme times a padded box a teacher drops from a 12 m balcony: h = -4.9t² + 12. To the nearest tenth, after how many seconds does it land?

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9th grade Quadratic word problems, and choosing a method worksheet – printable
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About this worksheet

Quadratic word problems, and choosing a method. Every version has 10 questions, and the answer key prints on the second page.

What your child will learn

  • I can set the height to 0 (or to a given height) and solve for the time.
  • I can throw out a negative length or time and say why.
  • I can pick square roots when x appears only inside a square.

Standard: A-CED.A.1, A-REI.B.4

Words to know

height formula: h = -16t² + vt + s gives a ball's height in feet after t seconds.

lands: Its height is 0 again, after the launch.

reject: Throw out a solution the story cannot use.

consecutive: Next to each other when counting, like 12 and 13.

border: A strip of the same width on every side.

Common mistakes

Your child gave the time the ball reaches its highest point, not the time it lands.

Your child gave t = 0, the moment the ball leaves the ground.

Your child kept a negative answer that does not fit the story.

What to say

Ask: is the ball on the ground at the top?

Ask: when does it come back down?

Ask: can a length or a time after the throw be negative?

Questions parents ask

What is the most common mistake with quadratic word problems, and choosing a method?

Your child gave the time the ball reaches its highest point, not the time it lands.

How can I help my child with quadratic word problems, and choosing a method?

Ask: is the ball on the ground at the top?

Are these 9th grade math worksheets free to print?

Yes. All 6 printable versions at each level are free to print, with the answer key, and no account is needed.

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