Question

Toto throws a ball up in the air. The height of the ball can be modelled using the equation h=-16.1t^2+73.5t+5.5 where t is time in seconds. At what time will the ball reach its maximum height? What is the maximum height? How long does it take for the ball to hit the ground?

Answer 1

as with any parabola ax^2+bx+c, the vertex is at

(-b/2a, (4ac-b^2)/4a)

it hits the ground when

-16.1t^2+73.5t+5.5 = 0

so plug in your quadratic formula.

Answer 2

for time to maximum height and that maximum height you need the vertex of this parabola.

Use the method you learned finding that vertex

as to hitting the ground, set
-16.1t^2+73.5t+5.5 = 0 and solve the quadratic.
reject any negative value of t.