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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

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

  1. Jun throws a basketball up from 4 feet at 48 feet per second. Its height is h = -16t² + 48t + 4. When does it land, in seconds to the nearest tenth?

  2. Kira kicks a soccer ball up from 3 feet at 56 feet per second. Its height is h = -16t² + 56t + 3. When does it land, in seconds to the nearest tenth?

  3. Luz tosses a play ball gently up from 5 feet at 24 feet per second. Its height is h = -16t² + 24t + 5. When does it land, in seconds to the nearest tenth?

  4. Milo's garden bed is 3 feet longer than it is wide, with an area of 54 square feet. Let x be the width, so x(x + 3) = 54. What is the width?

  5. Pia's poster is 6 inches taller than it is wide, with an area of 432 square inches. Let x be the width, so x(x + 6) = 432. What is the width?

  6. Ren's school banner is 7 feet longer than it is wide, with an area of 44 square feet. Let x be the width, so x(x + 7) = 44. What is the width?

  7. Tala opens a book to two facing pages. The page numbers multiply to 156. Call the smaller number n, so n(n + 1) = 156. What is the smaller number?

  8. Zee picks two consecutive even numbers that multiply to 224. Call the smaller number n, so n(n + 2) = 224. What is the smaller number?

  9. Ari picks two consecutive odd numbers that multiply to 255. Call the smaller number n, so n(n + 2) = 255. What is the smaller number?

  10. Bo's robot thinks of two consecutive whole numbers that multiply to 306. Call the smaller number n, so n(n + 1) = 306. What is the smaller number?

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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.

More algebra 1

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