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.

Question

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.

calculusxy · Answer

The height, when the ball reaches the ground, will be 0. So set the quadratic equation to zero: $0 = 80t - 16t^2 + 3.5$. When it's equal to zero, then it means that you should factor the equation and see what $t$ would equal to.