H=-16t^2+32t?

Question

so for this problem I'm supposed to find the max height of a ball thrown in the air from the given equation, and the time at which it reaches said height. Seems simple enough. h= height in ft and  t = time in sec. here's where I'm confused.... 
I started with -b / 2a to find the vertex (in this case -32 / 2(-16) . 
This gave me -32/ 32, which is just 1...
My instructor did this.... h = -16t (t - 2) 
She ended up with a time of 2 seconds. 
she plugged this into the equation and ended up with 32 ft... 
so her vertex was (2 , 32).... 

what's going on? Anybody know why we're getting two different answers?

Answer

A big part of math is pattern recognition. A lot of homework is just fighting with stuff so you will remember the pattern when you see it again. The most common pattern is (x + a) * (x + b) = x^2 + (a + b)x + ab and the special case (x + a) * (x - a) = x^2 - a^2. When you spot the pattern you can just write the answer from memory.

Now study this page until it seems obvious:  en.wikipedia.org/wiki/Polynomial_remainder_theorem

The teacher factored the equation. -16t^2+32t = -16t(t - 2) This is a procedure for finding zeroes, not peaks. The ball was at ground level at time zero and fell back to ground level at t=2. The vertex was in the middle at t=1. It looks like this:
 www.wolframalpha.com/input/?i=solve+y%3D-16t%5E2%2B32t

H=-16t^2+32t?

Answers (1)