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
