Question

A soccer ball is kicked into the air, and its path can be modeled with a quadratic function. The table shows the time, t, in seconds, and the height of the soccer ball, h, in feet. Follow the steps to write the function. 1. Identify x-intercepts: (0, 0) and (5, 0) 2. Use factored form: f(t) = a(t − 0)(t − 5) f(t) = at(t − 5) 3. Find the value of: 12 = a(3)(3 − 5) 4. Write function: f(t) = t(t −)

Answer 1

The answers -2 and 5

Answer 2

The y-intercepts are
(0,0) and (5,0)
The equation of the quadratic function is
f(t) = at(t-5)
Solving for a
12 = a(3)(3-5)
a = -2
The equation of the quadractic function is
f(t) = -2t(t -5)
f(t) = -2t² + 10t<span />