# Graphing reciprocals of quadratic functions

#### Everything You Need in One Place

Homework problems? Exam preparation? Trying to grasp a concept or just brushing up the basics? Our extensive help & practice library have got you covered.

#### Learn and Practice With Ease

Our proven video lessons ease you through problems quickly, and you get tonnes of friendly practice on questions that trip students up on tests and finals.

#### Instant and Unlimited Help

Our personalized learning platform enables you to instantly find the exact walkthrough to your specific type of question. Activate unlimited help now!

0/4
##### Examples
###### Lessons
1. Given that $f(x)=x^2-9$ , graph the reciprocal of the function $f(x)$
1. Given that $g(x)=2x^2+2x+1$, graph the reciprocal of the function $g(x)$
1. Given that $y=-2x^2+x+1$ , graph the reciprocal of $y$
1. Given that $f(x)=-x^2+2x-4$ , graph the reciprocal of the function $f(x)$
###### Topic Notes
We have learnt the basics of reciprocal functions. In this section, we will learn how to graph the reciprocal of a quadratic function, while applying the same principles we used when graphing the reciprocal of a linear function, while following the "6-steps Approach" noted below.
Steps to graph the reciprocal of a function:
1) Plot a horizontal asymptote
at
$y=0$
2) Plot vertical asymptote(s)
equate the original function to 0; solve for $x$
3) Plot y-intercept(s)
$\frac{1}{\text {y-intercept(s) of the original function}}$
4) Plot invariant points:
equate the original function to +1 and -1; solve for $x$
5) Plot
$\frac{1}{\text {vertex of the original function}}$
6) Place your pen at the invariant points, then smoothly move away while tracing along the asymptotes!