Horizontal Parabolas

The graph of the equation $LaTeX: y=a\left(x-h\right)^2+k\:$ $y=a\left(x-h\right)^2+k\:$ is a parabola with vertex $LaTeX: \left(h,k\right)\:$ $\left(h,k\right)\:$ and the vertical line $LaTeX: x=h\:$ $x=h\:$ as its axis of symmetry.

If we subtract LaTeX: k $k$ from each side of the equation $LaTeX: y=a\left(x-h\right)^2+k\:$ $y=a\left(x-h\right)^2+k\:$ , and interchange the roles of LaTeX: x-h $x-h$ and LaTeX: y-k, $y-k,$ the new equation also has a parabola as its graph.

Demo of subtracting k and interchanging x-h and y-k.PNG