Algebra 2 using quadratic equation

Question

An arrow is shot vertically upward from a platform 45 feet high at a rate of 168 ft/sec. Use the quadratic function h(t) = –16t2 + 168t + 45 find how long it will take the arrow to reach its maximum height, and then find the maximum height.

Answer 1

Since you probably do not yet have calculus, you need to know that the vertex of the parabola

Ax² + Bx + C occurs when x = -B/2A. I cannot prove this for you at this time!

In this case the vertex (and thus the maximum height) occurs when t=168/32=5.25, i.e. this is the time to reach maximum height.

Plug this value of t into the equation to get the maximum height.