The CHS Baseball team was on the field and the batter popped the ball up. The equation b (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 catch the ball before it hits the ground? Round to the nearest second.

What we are looking for is the time when the ball hits the ground. If the ball is on the ground, then b (x) = 0.

Solving for b (x) = 0:

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

0 = 80t - 16t^2 + 3.5

0 = - 16t^2 + 80t + 3.5

Solving the quadratic equation:

x = - 0.04 this answer is impossible since our time is negative

x = 5.04 which we can round round to 5 seconds

The catcher will have 5 seconds before the ball hits the ground.