1)When Twinkle Toes Tony kicked a football, it landed 100ft from where he kicked it. It also reached a height of 125 ft. Write an equation that, when graphed, will model the path of the ball from the moment it was kicked until it first touched the ground.

Question

2) A new skateboarder's ramp just arrived at Bungey's Family Fun Center. A cross -sectional view shows that the shape is parabolic. The sides are 12 ft high and 15 ft apart. Write an equation that, when graphed, will show the cross section of this ramp.

Answer 1

Both problems require to graph the vertex.
1. we know that the parabola passes through the following points: (0,0), (50,125),(100,0).
Using the standard formula, where (h,k) represent the coordinates of the vertex, we have h=50, k=125, and the parabola is:
y=a(x-h)^2+k=a(x-50)^2+125
Since the parabola passes through (0,0), we have
0=a(0-h)^2+k = ah^2+k = 2500a+125
=> a=-125/2500=-1/20
So parabola is
y=-(x-50)^2/20+125

(2) can be solved similarly.