Question

The function h(t) = –16t2 + 96t + 6 represents an object projected into the air from a cannon. The maximum height reached by the object is 150 feet.

After how many seconds does the object reach its maximum height?


2 seconds

3 seconds

6 seconds
9 seconds

Answer 1

Explanation:

This answer can be found in the h value for the vertex of a parabola, (h, k). The k value is the max height and we were already given that information. We need to solve for h. There's an easy way and a really complicated way...I'll show you the easy way because it's actually quite useful to know, especially when doing a lot of work with quadratics!

The formula to find h is

`h=(-b)/(2a)` and in our quadratic, a = -16, b = 96 and c = 6. Filling in what we need:

`h=(-96)/(2(-16))` so

h = 3

At 3 seconds the max height of 150 feet is reached.