Question

A boy kicks a ball in the air. The height y (in feet) above the ground of the ball is modeled by the equation y=-16x^2+80x, where x is the time (in seconds) since the ball was kicked. Find the roots of the equation when y=0. Explain what the roots mean in this situation. Can you please helpe me

Answer 1

The roots of the equation are at x=0 and x=5.

To solve this, we will factor the quadratic.  Both terms are divisible by 16x, so we will factor that out:

0=16x(-x+5)

Using the zero product property, we know that either 16x=0 or -x+5=0.  For the first choice, dividing both sides by 16 will give us x=0.

For -x+5=0, we will subtract 5 from both sides, giving us -x=-5.  Dividing both sides by -1, we have x=5.

The interpretation of the roots is the times when the ball hit the ground.  At x=0, this is before it is kicked.  At x=5, this is when the ball falls back to the ground.