Question

Suppose Paul kicks a soccer ball straight up into the air with an initial velocity of 96 feet per second. The function f(x) = -16t2 + 96t gives the height, in feet, of the soccer ball after t seconds. This function is shown in the graph below.
What do the x-intercepts represent in this real life situation in regards to the height of the soccer ball at that time?

Answer 1

We are told that the function f(t) outputs the height at t seconds.

The x-intercept is when y = 0. This is the same as saying when f(t) = 0.

When f(t) = 0, the height is 0, so the x-intercepts represent when the height is 0 and the soccer ball leaves the ground and lands back on the ground.