This week in math, we learned about reciprocal functions of parabolas. There are three forms of a reciprocal function graph for parabolas based on how many roots/where are the roots of a quadratic equation. They are similar to linear reciprocal functions, but a bit more complicated since there are can be up to two x-intercepts instead of just always having one with a linear function.

When we have a quadratic function with 2 x-intercepts like this: 

The reciprocal function looks like this: 

All values of x when y=1 and y=-1 are turned into the invariant points. The vertical asymptotes would be the original x-intercepts of the parent function (-5 and 1) and horizontal would be y=0.

When we have a quadratic function with no roots because it stays either below or above the x axis like this: The reciprocal function would look like this: 

Since there are no roots, there would be no vertical asymptote and the horizontal asymptote would be y=0. The invariant point would be the reciprocal of the y value of the vertex.

Finally, if you had a quadratic function with one root like:

The reciprocal function would look like this:

The invariant points would be where y=1 and and y=-1. The vertical asymptote would be the x value of the vertex and the horizontal asymptote would be y=0.