Question

A frog leaps 24 inches. The highest point in the jump is 6 inches. Assume the frog starts at (0,0). What quadratic function models the path of the jump?

Answer 1

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=-$\frac{1}{24} (x-12)^2+6$