Question

A baseball coach uses a pitching machine to simulate pop flies during practice. The quadratic function y=-16x² + 80x models the helght of the baseball after x seconds. How long is the baseball In the alr?

Answer 1

The ball is in the air for about 5 seconds.

Step-by-step explanation

The height of the baseball above the ground (y), as a function of the time is given as

y = -16x² + 80x

The question question then asks us to find how long the baseball was in the air.

So, basically, in mathematical terms, we need to find x, for when y > 0

y = -16x² + 80x

0 < -16x² + 80x

We can rewrite this

-16x² + 80x > 0

16x (-x + 5) > 0

Divide both sides by 16

x (-x + 5) > 0

So, we can find the solution of this inequality using the trial and error method.

x < 0 | 0 < x < 5 | x > 5

x | -ve | +ve | +ve

(-x + 5) | +ve | +ve | -ve

x(-x + 5) | -ve | +ve | -ve

So, we can see that the equation is greater than 0, that is, positive, when

0 < x < 5

So, the ball is in the air for about 5 seconds.

Hope this Helps!!!