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Practice

9.7.5 Practice

9.7.5 • Practice

Complete the following questions to practice the skills you have learned in this lesson.

  1. Mai and Jada are solving the equation 2 x 2 − 7 x = 15 using the quadratic formula.

Answer the following questions about the values of a , b , and c if this equation is written in standard form, a x 2 + b x + c = 0 .

  1. What is the value of a ?
  1. What is the value of b ?
  1. What is the value of c ?
  1. Mai and Jada are solving the equation 2 x 2 − 7 x = 15 using the quadratic formula but found different solutions.

    2. Mai's Method Jada's Method

    x = − 7 ± 7 2 − 4 ( 2 ) ( − 15 ) 2 ( 2 )
    x = − 7 ± 49 − ( − 120 ) 4
    x = − 7 ± 169 4
    x = − 7 ± 13 4
    x = − 7 + 13 4 = 6 4 = 3 2
    x = − 7 − 13 4 = − 20 4 = − 5

    x = − ( − 7 ) ± ( − 7 ) 2 − 4 ( 2 ) ( − 15 ) 2 ( 2 )
    x = 7 ± 49 − ( − 120 ) 4
    x = 7 ± 71 4

Who has the correct solution?

  1. Mai
  2. Jada
  3. Both of them
  4. Neither one
  1. The equation h ( t ) = − 16 t 2 + 80 t + 64 represents the height, in feet, of a potato t seconds after it was launched from a mechanical device.
  1. Choose the equation that would allow us to find the time the potato hits the ground.
  1. 0 = t 2 − 5 t − 4
  2. 0 = − 16 t 2 + 80 t + 64
  3. 0 = − t 2 − 5 t + 4
  4. 0 = 16 t 2 + 80 t + 64
  1. Solve the equation without graphing and write it down to find the approximate time the potato hits the ground rounded to one decimal place.
  1. Priya found x = 3 and x = − 1 as solutions to 3 x 2 − 6 x − 9 = 0 .
  1. If you check Priya's answer by substitution, is the answer correct?
  1. No
  2. Yes
  1. If you check Priya's answer by graphing, is the answer correct?
  1. No
  2. Yes
  1. If you check Priya's answer by using the quadratic formula, is the answer correct?
  1. No
  2. Yes
  1. A frog jumps in the air. The height, in inches, of the frog is modeled by the function h ( t ) = 60 t − 75 t 2 , where t is the time after it jumped, measured in seconds.
  1. Select two solutions to the equation 60 t − 75 t 2 = 0 .
  1. 0
  2. 4 5
  3. 5
  4. 1
  5. − 1 5
  1. What do the solutions tell us about the jumping frog? Select two that apply.
  1. The frog landed 1 seconds after it jumped and was on the ground again.
  2. The frog landed 4 5 seconds after it jumped and was on the ground again.
  3. The height of the frog was 5 inches before it jumped.
  4. The negative solution shows how far down the frog was before it jumped.
  5. The height of the frog was 0 inches before it jumped.
  1. A tennis ball is hit straight up in the air, and its height, in feet above the ground, is modeled by the equation f ( t ) = 4 + 12 t − 16 t 2 , where t is measured in seconds since the ball was thrown.
  1. Select two solutions to the equation 0 = 4 + 12 t − 16 t 2 .
  1. 1 4
  2. 4
  3. 16
  4. 1
  5. − 1 4
  1. What do the solutions tell us about the tennis ball? Select two that apply.
  1. The ball hits the ground 1 4 second after it is hit.
  2. The negative solution does not have meaning because a negative value for time does not make sense.
  3. The ball hits the ground 1 second after it is hit.
  4. The negative solution is a result of the bounce of the ball.
  5. The ball hits the ground − 1 4 second after it is hit.