GIVING 30 POINTS!! A skateboard halfpipe is being designed for a competition. The halfpipe will be in the shape of a parabola and will be positioned above the ground such that its focus is 40 ft above the ground. Using the ground as the x-axis, where should the base of the halfpipe be positioned? Which equation best describes the equation of the halfpipe?

y = (1/80)x^2 +20

Step-by-step explanation:

Assuming the halfpipe is only useful if the curve opens upward, the "base" (vertex) must be below the focus, so cannot be at (0, 40).

Apparently, the ground is supposed to be the directrix of the curve. Then the vertex is halfway between the focus and the ground, so is at (0, 20). The focus-vertex distance (p) is then 40-20 = 20 so the coefficient of the squared term is 1/(4p) = 1/(4·20) = 1/80.

For a vertex of (0, 20) and a vertical scale factor of 1/80, the equation of the curve is y = (1/80)x^2 +20

x -

median = 1.25

range = 12-14.5

interquartile = q12-q14.5

y -

median = 1

range = 15-17

interquartile = q15-q17