Question

A ball is thrown into the air with an upward velocity of 36 ft/s. Its height h in feet after t seconds is given by the function h = –16t2 + 36t + 9. a. In how many seconds does the ball reach its maximum height? Round to the nearest hundredth if necessary. b. What is the ball’s maximum height

Answer 1

We know that the height h in feet of the ball after t seconds is given by the function h=-16t^2+36t+9.
f(x)=ax^2+bx+c
From the function we know that the graph is a parabola and
because of the negative lead coefficient we know that the parabola is opening down.
a.x=-b/2a=-36/(-32)=36/32=1.125 In 1.125 seconds the ball will reach its maximum height.
b. The maximum height is: f(1.125)