Suppose you are asked to design the first ascent and drop for a roller coaster. You decide to make the slope of the ascent .8 and the slope of the drop -1.6. You then decide to connect these two straight stretches y=L1 and y=L2 with part of a parabola f(x) = ax^2 + bx + c, where x and f(x) are measured in feet. For the track to be smooth, there can't be any abrupt changes in direction, so you want the linear segments L1 and L2 to be tangent to the parabola at the transaction points P and Q. To simplify the equations, you decide to place P at the origin
QUESTIONS
1) Suppose the horizontal distance between P and Q is 100ft. Write equations in a, b, and c that will ensure that the track is smooth at the transition points.
2) Solve the equations in part (2) for a, b, and c to find a formula for f(x) f(x) = ?
3) Find the elevation of point Q to find an equation for L2