Quadratic Function

Question

A person standing close to the edge on top of a 112-foot building throws a ball vertically upward. The quadratic function h(t) = −16t^2 + 96t + 112 models the ball's height about the ground, h(t), in feet, t seconds after it was thrown.

a) What is the maximum height of the ball?

(Round your answer to the nearest hundredths.)

b) How many seconds does it take until the ball hits the ground?

Answer 1

a) max h(t) happened when t = - 96/(-16·2) = 3 s

hmax = - 16·9 + 96·3 + 112 = 256 feet;

b) At the ground h(t) = -16t² + 96t + 112 = 0; t² - 6t - 7 = 0; (t - 7)(t + 1) = 0;

t = 7 s