Question

The CHS baseball team was on the field and the batter popped the ball up. The equation f(x)=80t-16t^2+3.5 represents the height of the ball above the ground in feet as a function of time in seconds. How long will the catcher have to get in position to get to the ball before it hits the ground?

Answer 1

The catcher has less than 5 seconds to get the ball

Explanation:

we have

`f(x)=80t-16t^(2) +3.5`

This is a vertical parabola open down

we know that

The ball hit the ground when f(x)=0 -----> x-intercept of the function

Remember that the x-intercept of the function is the value of x when the value of the function is equal to zero

so

using a graphing tool

The x-intercept is for t=5 sec

see the attached figure

therefore

The catcher has less than 5 seconds to get the ball