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Use the table to answer the question.

Seconds, x 0 1 1.5 2 3
Height, y 8.75 10.75 11 10.75 8.75
Jen is trying different techniques to improve her free throws. Her old technique could be modeled by the equation y=−1.25(x−2)2+10.5
, where the input is the amount of time, in seconds, after throwing the ball, and the output is the height of the ball, in feet, above the ground. Her new technique can be modeled by the table. Assuming Jen is more successful with her free throws the higher she throws the ball, which technique should she choose for maximal success?

(1 point)
Responses

Jen should choose the old technique since it gives the ball a maximum height of 10.5 feet.
Jen should choose the old technique since it gives the ball a maximum height of 10.5 feet.

Jen should choose the new technique since it gives the ball a maximum height of 11 feet.
Jen should choose the new technique since it gives the ball a maximum height of 11 feet.

Jen should choose the new technique since it gives the ball a maximum height that is more than 6 inches higher than the old technique.
Jen should choose the new technique since it gives the ball a maximum height that is more than 6 inches higher than the old technique.

Jen should choose the old technique since it gives the ball a maximum height that is 6 inches higher than the new technique.

1 answer

To compare Jen's old and new techniques based on the maximum height of the ball:

  1. Old Technique: The maximum height according to the equation \( y = -1.25(x - 2)^2 + 10.5 \) occurs at the vertex of the parabola. The vertex of this parabola is at \( x = 2 \), and substituting \( x = 2 \) into the equation gives: \[ y = -1.25(2 - 2)^2 + 10.5 = 10.5 \text{ feet.} \]

  2. New Technique: From the table, the maximum height recorded is:

    • At \( x = 1.5 \): \( y = 11 \text{ feet.} \)

Comparing the two techniques:

  • Old technique maximum height: 10.5 feet
  • New technique maximum height: 11 feet

Since 11 feet (new technique) is greater than 10.5 feet (old technique), Jen should choose the new technique because it allows the ball to reach a higher maximum height.

Therefore, the correct response is: Jen should choose the new technique since it gives the ball a maximum height of 11 feet.