I can't figure out this word problem

Question

A ball was kicked into the air from a balcony 20 feet above the ground, and the ball’s height above theground, in feet, t seconds after the ball wasw kicked was 2 h(t) = 20− 16t+ 32t. What was the maximum height, in feet, of the ball above the ground after it was kicked?

Answer 1

I believe your equation is supposed to read:

h(t) = -16t² + 32t + 20

 

This is a parabola opening downward as should be expected.

 

Since the parabola opens down the maximum height is at

the vertex of the parabola as given from the equation.

From the quadratic equation  at² + bt + c ...  a=-16, b=32, c=20

The vertex will be at the point  (-b/2a , h(-b/2a))

 

-b/2a = -32/((2(-16)) = -32/-32 = 1

h(1) = -16(1²) + 32(1) + 20 = 36

 

Vertex is at (1, 36) meaning that the maximum height of 36 ft

 is achieved 1 second after the ball was kicked