We were given the following information:
65 degree launch angle from the horizontal The initial velocity: 92 ft./sec. The height of the tower: 160 ft. 
For this problem we are solving for the vertex and the xintercepts:
Unknown peak of the fireworks Unknown distance it will travel 
We created a diagram including all the information we were given.

At first for the vertex, I thought about using the equation h(t)=160+92t16t^2 and dividing it by 2 and squaring it. But then I ran into a bump and asked why it wasn't working. Then we realized that there was something different about the equation. That it had a number for a=16 instead of just being x an unknown number. So what we had to do instead was get the middle point of 0 to the positive x intercept. Because the launch happens on point 0 not a negative point; this gives us the x intercept. Then we plugged in that sum into the equation for t ; which then gave us the y intecept. 