Quadratics Word Problem

Question

The height y(in feet) of a basketball t seconds after it is thrown can be modeled by the function y = -16t^2 +32t +2. The player shooting the basketball throws an air ball, how long is the ball in the air for?

Answer 1

This question is related with finding the vertex or maximum point of the curve. So we would use the formula:

-b/2a for x coordinate of the maximum point.

Remember: y=ax^2+bx+c

a=-16

b=32

c=2

-b/2a= -32/2*(-16)= 1

This means it will take 1 second for the basketball to reach the highest point and then 1 second to land. SO totally the ball is in the air for 2 seconds.