The path is in the shape of a parabola, the horizontal length is 24, so the middle point is at x=12, the symmetry line is x=12, the highest point (the vertex) is at (12,6)
the equation in vertex form is y=a(x-12)²+6
next, find a by using either one of the two points, the starting point (0,0) or the end point (0,24). obviously (0,0) is easier to calculate:
0=a(0-12)² +6
a=-1/24
so the quadratic equation is y=-
Answer:

Step-by-step explanation:

Solve the lower equation first
+12 on each side
7x=51
divide by 7
x=51/7
then use that to solve the upper equation

Method 1.
Use 

Method 2.

The solution to this equation is the number 8