Question

Emmy throws a doggy toy up in the air. The path of the toy is modeled by the function f(x)=−x^2+4x+5, where x is the number of feet the toy is from Emmy and f(x) is the height of the toy. What is the maximum height of the toy?

Answer 1

9feet

Explanation:

Given the path of the toy modeled by the function f(x)=−x^2+4x+5, where x is the number of feet the toy is from Emmy and f(x) is the height of the toy.

AT maximum height, the velocity of the toy will be zero. Hence;

df(x)/dx = 0

-2x + 4 = 0

-2x = -4

x = -4/-2

x = 2

Get the maximum height;

Substitute x = 2 into the given function;

f(x)=−x^2+4x+5

f(2)=−2^2+4(2)+5

f(2) = -4+8+5

f(2) = 9feet

Hence the maximum height of the toy is 9feet