Question

An object is launched upward at 64 ft/sec from a platform that is 80 feet high. What is the objects maximum height if the equation of height (h) in terms of time (t) of the object is given by h(t) = -16t² + 64t + 80?
Round to the nearest foot.

Answer 1

there are several ways to do this question

1. calculus

2 algebra..

Answer 2

notice that, h(t) = -16t² + 64t + 80 <-- is a parabola
the HIGHEST or LOWEST point for a parabola, is at its vertex

x = seconds or TIME
y = feet, or HEIGHT

to get the vertex of a parabola likewise, you can find it at \(\bf \left(-\cfrac{b}{2a}\quad ,\quad c-\cfrac{b^2}{4a}\right)\)

you only need height, so only use the y-coordinate part :)


unless as campbell_st said, you'd need it using calc, for which you'd need to first get the derivative of it