Highway Design In order to build a highway, it is
necessary to fill a section of a valley where the grades (slopes)
of the sides are 9% and 6% (see figure). The top of the filled region will have the shape of a parabolic arc that is tangent to
the two slopes at the points and The horizontal distances from to the -axis and from to the -axis are both 500 feet.

(a) Find the coordinates of and
(b) Find a quadratic function for
that describes the top of the filled region.

Question

Highway Design In order to build a highway, it is
necessary to fill a section of a valley where the grades (slopes)
of the sides are 9% and 6% (see figure). The top of the filled region will have the shape of a parabolic arc that is tangent to
the two slopes at the points and The horizontal distances from to the -axis and from to the -axis are both 500 feet.

(a) Find the coordinates of and
(b) Find a quadratic function for
that describes the top of the filled region.

mathmate · Answer

It looks like some information is missing in the question, and a diagram too.
"...The horizontal distances from to the ?-axis and from ? to the ?-axis are both 500 feet."
and
"(a) Find the coordinates of ?  and..."