Graphing reciprocals of quadratic functions

All in One Place

Everything you need for better grades in university, high school and elementary.

Learn with Ease

Made in Canada with help for all provincial curriculums, so you can study in confidence.

Instant and Unlimited Help

Get the best tips, walkthroughs, and practice questions.

0/4
?
Examples
Lessons
  1. Given that f(x)=x2−9f(x)=x^2-9 , graph the reciprocal of the function f(x)f(x)
    1. Given that g(x)=2x2+2x+1g(x)=2x^2+2x+1, graph the reciprocal of the function g(x)g(x)
      1. Given that y=−2x2+x+1y=-2x^2+x+1 , graph the reciprocal of yy
        1. Given that f(x)=−x2+2x−4f(x)=-x^2+2x-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
          at
          y=0y=0
          2) Plot vertical asymptote(s)
          equate the original function to 0; solve for xx
          3) Plot y-intercept(s)
          1y-intercept(s) of the original function\frac{1}{\text {y-intercept(s) of the original function}}
          4) Plot invariant points:
          equate the original function to +1 and -1; solve for xx
          5) Plot
          1vertex of the original function\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!