Question

An archway is modeled by the equation y = -2x2 + 8x. A rod is to be placed across the archway at an angle defined by the equation x − 2.23y + 10.34 = 0. If the rod is attached to the archway at points A and B, such that point B is at a higher level than point A, at what distance from the ground level is point B?

Answer 1

This is a fun problem!  Just graph the two equations, then see what points the line intersects with the parabola.  Or, set the two equations equal to each other, and solve for the two intersecting points.
Solve for x and y:       -2x+8 = x-2.23y+10.34