How to Graph Quadratic Inequalities? (+FREE Worksheet!)

Want to know how to graph Quadratic inequalities? You can do it in a few simple and easy steps.

How to Graph Quadratic Inequalities? (+FREE Worksheet!)

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Step by step guide to Graphing Quadratic inequalities

  • A quadratic inequality is in the form \(y>ax^2+bx+c\) (or substitute \(<,≤,\) or \(≥ \) for \(>\)).
  • To graph a quadratic inequality, start by graphing the quadratic parabola. Then fill in the region either inside or outside of it, depending on the inequality.
  • Choose a testing point and check the solution section.

Graphing Quadratic inequalities – Example 1:

Sketch the graph of \(y>3x^2\).

Answer:

First, graph \(y=3x^2\)
Since the inequality sing is \(>\), we need to use dash lines.
Now, choose a testing point inside the parabola. Let’s choose \((0,2)\).
\(y>3x^2→2>3(0)^2→2>0\)
This is true. So, inside the parabola is the solution section.

Graphing Quadratic inequalities – Example 2:

Sketch the graph of \(y>2x^2\).

Answer:

First, graph \(y=2x^2\)
Since the inequality sing is \(>\), we need to use dash lines.
Now, choose a testing point inside the parabola. Let’s choose \((0,2)\). \(y>2x^2→2>2(0)^2→2>0\)
This is true. So, inside the parabola is the solution section.

Exercises for Graphing Quadratic inequalities

Sketch the graph of each function.

  • \(\color{blue}{y<-2x^2}\)
  • \(\color{blue}{y≥4x^2}\)
  • \(\color{blue}{y<-2x^2}\)
  • \(\color{blue}{y≥4x^2}\)

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