Algebra II

Question

A projectile is thrown upward so that its distance above the ground after t seconds is h(t) = -16t² + 456t. After how many seconds does it reach its maximum height? Round your answer to the nearest second.
Question 12 options:

1) 28.5 sec

2) 9 sec

3) 38 sec

4) 14 sec

Answer 1

The maximum height is the y-coordinate of the vertex of the graph of this equation.

 

Let a = -16 and b = 456. The x-coordinate of the vertex is -b/(2a) = -456/[2(-16)] = 57/4.

 

When you plug this into the function, you'll get the y-coordinate and the height.

 

h(57/4) = 3249 feet.

 

The maximum height is 3249 ft. (You did not specify height units, but your equation assumes feet and seconds.)