the height of the ball in meters is modeled by f(x)= -5x^2+40x, where x is the time in seconds after it is hit. How long is the ball in the

We can also attack this by noting that f(x) will be zero when the ball lands as well as when it starts.

-5x² + 40x = 0

x*(-5x + 40) = 0

so x=0 (start)

and -5x + 40 = 0 or 5x = 40 or x = 8 (when it lands).

The flight of the ball is a parabola.

If we take the first derivative of the function, we can find the time when the ball reaches a maximum height

f'(x) = -10x +40      And setting this to 0, we have

-10x + 40 = 0         x = 4 sec

And it will take 4 more seconds to land, so it was in the air for 8 secs.

Verify this: At 0 secs. the height was 0, and at 8 secs. the height is, -5*8^2 + 40*8 = 0