Question

A diver jumps up and over from a cliff in order to avoid rocks and land in the deeper water. The path of the dive can be modeled using the function f(x)=−16x2+2x+48, where f(x) is the height, in feet, of the diver at x time in seconds. What is the maximum height, in feet, the diver will reach? Round your answer to the nearest hundredth if necessary. Do not include units in your answer.

Answer 1

48.06 to the nearest hundredth.

Explanation:

f(x) = -16x^2 + 2x + 48

To find the maximum height we convert to vertex form:

= -16(x^2 + 1/8x) + 48

= -16[x + 1/16)^2 - 1/256] + 48

= -16(x + 1.16)^2 + 16/256 + 48

= 48.0625.