Question

A golf ball is struck by a​ 60-degree golf club at an initial velocity of
84
feet per second. The height of the golf ball in feet is given by the quadratic function h(x)= 16 x^2/(42)^2+72.7/42x where x is the horizontal distance of the golf ball from the point of impact. What is the horizontal distance of the golf ball from the point of impact when the ball is at its maximum​ height? What is the maximum height obtained by the golf​ ball?

Answer 1

I think you are missing a minus sign on the x^2 term, since g = -32 ft/s^2

h(x) = 1/42 (-16/42 x^2 + 72.7x)
= x/42 (-16/42 x + 72.7)
h=0 when x=0 (ball is hit), and when
x = 190.8 (ball lands)
The symmetry of a parabola means that the ball is at its highest midway between the two roots.

Just plug that in to find the max height.

http://www.wolframalpha.com/input/?i=-16+x^2%2F%2842%29^2%2B72.7%2F42x

Answer 2

330.2657