Graphing reciprocals of quadratic functions

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Given that $f(x)=x^2-9$ $f (x) = x^{2} - 9$ , graph the reciprocal of the function $f(x)$ $f (x)$
Given that $g(x)=2x^2+2x+1$ $g (x) = 2 x^{2} + 2 x + 1$ , graph the reciprocal of the function $g(x)$ $g (x)$
Given that $y=-2x^2+x+1$ $y = - 2 x^{2} + x + 1$ , graph the reciprocal of $y$ $y$
Given that $f(x)=-x^2+2x-4$ $f (x) = - x^{2} + 2 x - 4$ , graph the reciprocal of the function $f(x)$ $f (x)$

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

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!

Graphing reciprocals of quadratic functions

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Topic Notes

Graphing reciprocals of quadratic functions

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