Quadratic word problems, and choosing a method

Answer Key - Grade 9 Math Worksheet - Building Confidence

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

1. 1.

   Esme tosses a striped play ball straight up at 48 feet per second. Its height in feet is h = -16t² + 48t. It lands when h = 0. When does it land, in seconds?

   3
2. 2.

   Luz launches a toy foam rocket straight up at 56 feet per second. Its height in feet is h = -16t² + 56t. It lands when h = 0. When does it land, in seconds?

   3.5
3. 3.

   Milo's garden bed is x meters wide. Solving x² + 3x - 40 = 0 gives x = 5 or x = -8. Which answer fits the story?

   • x = -8
   • Neither one fits
   • x = 5, because a width must be positive
   • Both x = 5 and x = -8, since both come from the equation
4. 4.

   Noah's rug is x feet long. Solving x² + 2x - 63 = 0 gives x = 7 or x = -9. Which answer fits the story?

   • Both x = 7 and x = -9, because both answers work in the equation
   • x = -9
   • x = 7, because a length must be positive
   • Neither one fits
5. 5.

   Pia throws a ball from a balcony. It lands when 16t² - 32t - 20 = 0, so t = 2.5 or t = -0.5. Which answer fits the story?

   • Both t = 2.5 and t = -0.5, since both come from the equation
   • t = -0.5
   • t = 2.5, because a time must be positive
   • Neither one fits
6. 6.

   Ren's square quilt patch is x inches on a side. Solving x² - x - 30 = 0 gives x = 6 or x = -5. Which answer fits the story?

   • x = -5
   • x = 6, because a side must be positive
   • Both x = 6 and x = -5
   • Neither one fits
7. 7.

   Tala wants to solve one of these by square roots, with no factoring. Which can be solved by taking square roots?

   • x² + 4x = 12
   • x² - 5x + 6 = 0
   • 3x² - 12 = 0
8. 8.

   Zee will solve one of these by square roots, with no factoring. Which can be solved by taking square roots?

   • x² - 2x = 25
   • (x - 2)² = 25
   • x(x - 2) = 25
9. 9.

   Ari's robot can only take square roots. Its list has three equations. Which can be solved by taking square roots?

   • x² + 5x - 80 = 0
   • 5x² + x = 80
   • 5x² = 80
10. 10.

    Bo's math book asks for square roots only, no factoring. Which can be solved by taking square roots?

    • x² + 9x + 45 = 0
    • x² + 9x = 45
    • x² + 9 = 45