velocity height vertex

Question

If a football is kicked straight up with an initial velocity of 64 ft/sec from a height of 6 ft, then its height above the earth is a function of time given by h(t)=-16t^2+64t+6. What is the maximum height reached by this ball? Hint: Find the vertex of the graph of the quadratic function. 

The maximum height reached by the ball is _ ft. 

 

help is greatly appreciated, thank you!

Answer 1

We can put h(t) in vertex form.

 

h(t) = a(t - r)² + k

 

where:

a is the coefficient of the x² term

The vertex is (r, k) and is also the maximum

 

 

h(t) = -16(t² - 4t + 4) + 70

h(t) = -16(t - 2)(t - 2) + 70

h(t) = -16(t - 2)² + 70

 

 

r = 2

k = 70

 

The maximum height is the value of k.