# Week 13 – Absolute Values and Reciprocal functions of Quadratic Equations

This week we learned how to graph absolute values and reciprocal functions of quadratic equations, it is quite similar to linear equations.

Much like linear equations, we should draw our original graph first $(y=x^2-3)$

The quadratic absolute value graph is very similar to the linear absolute value graph, it bounces up from $y=0$

The reciprocal value graph is a bit more complicated and difficult to graph because of all the fractions you get from $y=\frac{1}{x^2-3}$ Something to note is that the asymptotes (the invisible lines between the yellow lines) will never touch $y=0$ and the the x intercept which in this case is $x=0$

Here are some other quadratic reciprocal graphs with different y intercepts

$y=x^2$

$y=(x+3)^2+3$

As you can see different amounts of invariant points (where y is equal to either 1 or -1) changes the shape of the reciprocal function.