Question

A basketball is thrown from the roof of a 50 foot building. It reaches a maximum height of 86 feet 1.5 seconds after the ball is thrown. Write a function representing the problem situation in vertex form, f(x)=a(x-h)^2+k, and standard form, f(x)=a^2+bx+c.

Answer 1

Step-by-step explanation:

The basketball reaches a maximum height of 86 feet after 1.5 seconds, so the vertex is (1.5, 86).

f(x) = a(x − 1.5)² + 86

We know the initial height is 50 feet, so plug in the point (0, 50) to find the value of a.

50 = a(0 − 1.5)² + 86

-36 = 2.25a

a = -16

f(x) = -16(x − 1.5)² + 86

Simplify to get the standard form.

f(x) = -16(x − 1.5)² + 86

f(x) = -16(x² − 3x + 2.25) + 86

f(x) = -16x² + 48x − 36 + 86

f(x) = -16x² + 48x + 50