Question

H = -16t^2 + 36t + 56 Where H is the height of the ball after t seconds have passed.

Answer 1

we have the equation

H = -16t^2 + 36t + 56

This equation represents a vertical parabola open downward, which means, the vertex is a maximum

The time t when the ball reaches its maximum value corresponds to the x-coordinate of the vertex

so

Convert the given equation into vertex form

H=a(t-h)^2+k

where

(h,k) is the vertex

step 1

Complete the square

H = -16t^2 + 36t + 56

Factor -16

H=-16(t^2-36/16t)+56

H=-16(t^2-36/16t+81/64)+56+81/4

Rewrite as perfect squares

H=-16(t-9/8)^2+76.25

the vertex is (9/8,76.25)

therefore

the time is 9/8 sec or 1.125 seconds when the ball reaches its maximum