A building has an entry the shape of a parabolic arch 22 ft high and 28 ft wide at the base as shown below.

A parabola opening down with vertex at the origin is graphed on the coordinate plane. The height of the parabola from top to bottom is twenty two feet and its width from left to right is twenty eight feet.

Find an equation for the parabola if the vertex is put at the origin of the coordinate system.

Question

A building has an entry the shape of a parabolic arch 22 ft high and 28 ft wide at the base as shown below. 

A parabola opening down with vertex at the origin is graphed on the coordinate plane. The height of the parabola from top to bottom is twenty two feet and its width from left to right is twenty eight feet. 

Find an equation for the parabola if the vertex is put at the origin of the coordinate system.

mathmale · Answer

I'd strongly suggest that you sketch this inverted parabola (or share with us the sketch that came with this problem).  Label the vertex.  Using the fact that the arch is 22 feet high and the width of the entire parabola is 28 feet, find the point at which the right arc of the parabola touches the ground.

Next, look up (if necessary) and write out the equation for a parabola with vertex at (h,k).

Once you've done that, we'll address the next step or two.