Graphing Quadratic inequalities

Graphing Quadratic inequalities

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

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.

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 \((0,2)\).
\(y>3x^2→2>3(0)^2→3>0\)
This is true. So, inside the parabola is the solution section.

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

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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