Question

The height off the ground, in feet, of a squirrel leaping from a tree branch is given by the function H(x) = –16x*2 + 24x + 15, where x is the number of seconds after the squirrel leaps. How many seconds after leaping does the squirrel reach its maximum height?

A.

1. 33 s


B.

0. 50 s


C.

0. 75 s


D.

1. 00 s

Answer 1

C. 0.75 s

Explanation:

Given a squirrel's height is defined by H(x) = -16x² +24x +15, you want to know the value of x when the height is a maximum.

Vertex

The x-coordinate of the vertex of y = ax² +bx +c is x=-b/(2a). For the given function, we have a=-16 and b=24, so the x-value at the vertex is ...

x = -b/(2a) = -24/(2(-16)) = 24/32 = 3/4

x = 0.75

The squirrel reaches its maximum height 0.75 seconds after leaping.