Question

Quadratic Function help?

Answer 1

A) The T-shirt will be at its maximum height when the velocity is at zero, because its velocity will be at zero when it reaches the top of its arc.
You have the position function, y= -16t^2 + 72t + 5, so the velocity function is its derivative, v= -32t + 72.
Set that equal to zero, 0= -32t + 72, and solve for t.
0= -32t + 72
32t = 72
t = 9/4 or 2.25 seconds.

b) Plug what you found in part a) back into your position equation.
-16(2.25)^2 + 72(2.25) + 5 = -81 + 162 + 5 = 86 feet

c) The t-shirt's lowest point is 5 feet above the ground (that's the '+ 5' in the position equation) and its highest point is 86 feet, which you found in part b). So the range is [5,86]