What is the maximum height of h(t)=-16t^2+16t+480

There's a negative in a, so it would have an invisible -1 multiplying the whole equation.

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.

Start to factor them by adding brackets and using GCF to separate them.

Again, with GCF to simplify even more.

And re-arrange to form the numbers into factored form cause of distributive property.

GCF to simplify to lowest terms.

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.

Take the midpoint and plug into your quadratic equation to find your max height. Use a calculator for this.

The first one is 2/3the second is 1/160the third is 4/125