There's a negative in a, so it would have an invisible -1 multiplying the whole equation.
![-1(16t^2-16t-480)](https://tex.z-dn.net/?f=-1%2816t%5E2-16t-480%29)
Then you take two numbers that multiply to 16*-480
and add to -16.
Let's hide out the -1 for now until the end to make it easier for us.In this case, it would be -96 and 80 because 16*-480 = -7680 and multiplying -96 by 80 results in same product while adding up to -16.
Then you put those numbers in.
![(16t^2-96t+80t-480)](https://tex.z-dn.net/?f=%2816t%5E2-96t%2B80t-480%29)
Start to factor them by adding brackets and using GCF to separate them.
![(16t^2-96t)+(80t-480)](https://tex.z-dn.net/?f=%2816t%5E2-96t%29%2B%2880t-480%29)
Again, with GCF to simplify even more.
![16t(t-6)+80(t-6)](https://tex.z-dn.net/?f=16t%28t-6%29%2B80%28t-6%29)
And re-arrange to form the numbers into factored form cause of distributive property.
![(16t+80)(t-6)](https://tex.z-dn.net/?f=%2816t%2B80%29%28t-6%29%20)
GCF to simplify to lowest terms.
![16(t+5)(t-6)](https://tex.z-dn.net/?f=16%28t%2B5%29%28t-6%29)
Bring back the -1 we hid.
Important Note: in vertex and factored form, the plus/positive signs within the brackets mean left side into negative x-values, and negative signs within brackets mean right side into positive x-values. In this case, your x-intercepts/zeros are (-5,0) and (6,0).
A person can't go into negative time, so they start from 0 and hit into the positive number of the x-int, so that's (6,0). 6 seconds. Find midpoint by adding the two x-int and dividing by 2.
![h= \frac{-5+6}{2} \\ \\ h= \frac{1}{2}](https://tex.z-dn.net/?f=h%3D%20%5Cfrac%7B-5%2B6%7D%7B2%7D%20%5C%5C%20%20%5C%5C%20h%3D%20%5Cfrac%7B1%7D%7B2%7D)
Take the midpoint and plug into your quadratic equation to find your max height.
Use a calculator for this.