Richard tosses a ball into the air. The function h(t) = −5t2 + 10t + 6 gives the approximate height h, in meters, of the ball t seconds after he tosses it. Does the ball reach a height of 12 m?

Answer 1

No, it's just short by 1 meter.

You can take the derivative, set it = 0 and solve to find the time (t) where the curve has a max. Then plug that into the function to find the max ht.

or, the t value of the vertex is given by -b/2a or -10/(2)(-5) = 1 sec

then ht = -5 + 10 + 6 = 11 meters max. ht. after 1 sec.

Check it out on the Desmos Graphing Calculator website.