Hard problem : Equation of ..
I have no idea where to start.
"A parabolic segment of a roller coaster track is to join two inclined segments of track. The incoming track has a slope of -4/3 and the slope at the end of the curve is to have a slope of 2/3. The parabolic portion of the curve must start at a height of 30 feet and end after 50 feet of horizontal distance."
A) Find the equation of the parabolic portion of the track.
B) Find the height of the track where the parabola joins the line with a slope of 2/3.
I know the equation for a parabola is y = ax^2 + bx + c.. &the derivative is y' = 2ax + b, but that's as far as I've gotten.