Essentially, when it's asking "find the maximum height and the time it occurs at," it wants you to use the vertex formula. This is a formula that gives you the x-coordinate of the vertex, or the maximum or minimum height of a parabola.
x-coord of vertex =
A quadratic equation is structured with 3 parts
for this one, a = -16, b = 104, c = 5
finding the x-coord just plug those into the formula
simplify to
- 104/ - 36
negative cancels
104/32
at time = 13/4, there is a relative maximum.
to find its height, just plug that value into your calculator using the original equation
plugging in t = 13/4 yields a value of 174
Coords of rel. max. (13/4 , 174)