Suppose you are asked to design the first ascent and drop for a roller coaster.

Question

Suppose you are asked to design the first ascent and drop for a roller coaster. You decide to make the slope of the ascent 0.8 and the slope fo the drop -1.6. You decide to connect these two stretches y=L1(x) and y=L2(x) with part of a parabola y = f(x) = ax^2 + bx + c, where x is measured in feet. For the track to be smooth, there can't be abrupt changes so you want the linear segments L1 to be tangent to the parabola at the transition points P and L2 to be tangent to the parabola at point Q. P is the origin. Suppose the horizantal distance between P and Q is 100 ft. Write equations in a,b, and c that will ensure the track is smooth at the transition points. Solve the equation for a,b, and c to find the formula for f(x)

Explanation / Answer

For the track to be smooth there can

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