U3.L4.HW: Quadratic Functions: Question 22

Question

Answer first. Explain the answers afterwards.

A person standing close to the edge on top of a 56-foot building throws a ball vertically upward. The quadratic function h(t) = -16t² + 104t + 56 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?

________ feet

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

________ seconds

Answer 1

The maximum height of the ball will be where the y-coordinate of the vertex is located:

x = -b/2a = -104/(2(-16)) = -104/(-32) = 13/4

h(13/4) = 225

Hence, the ball will reach its maximum height of 225 feet after it is thrown.

h(t) = -16t² + 104t + 56

0 = -16t² + 104t + 56

0 = (-16x-8)(x-7)

We can only consider x=7 as that is the only positive solution since time can't be negative, so the ball will hit the ground after 7 seconds.

Hope these answers and explanations helped!