Question

A tennis ball is hit over a fence; the path that the ball follows can be expressed by the equation y=−14x2+8x
, where x represents the horizontal distance and y is the vertical height. In terms of the context, determine the maximum height reached by the tennis ball.(1 point)
Responses

16 feet
16 feet

64 feet
64 feet

8 feet
8 feet

32 feet

Answer 1

The parabola's vertex gives the maximum. For y = −14x^2 + 8x the x-coordinate of the vertex is x = −b/(2a) = −8/(2·(−14)) = 2/7. Plugging in,

y = −14(2/7)^2 + 8(2/7) = −14·4/49 + 16/7 = −8/7 + 16/7 = 8/7 ≈ 1.14 feet.

So the maximum height is 8/7 feet (≈1.14 ft). None of the listed choices (16, 64, 8, 32 feet) are correct.