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Graphing Quadratic Inequalities

Graphing Quadratic Inequalities 1.10 - Solution

arrow_back Return to Graphing Quadratic Inequalities

We will graph the given quadratic inequality then we will find the error Stella-Jon spotted in Ron-Jon's solution. To graph the quadratic inequality, we will follow three steps.

  1. Graph the related quadratic function.
  2. Test a point not on the parabola.
  3. Shade accordingly. If the point satisfies the inequality, we will shade the region that contains the point. If not, we will shade the opposite region.

Step

Let's draw the graph of the related function, which is If you need explanations on graphing parabolas, please refer to this exercise.

Step

Next, let's determine which region to shade by testing a point. For simplicity, we will use as our test point. Let's see if it satisfies the given inequality.

Step

Since produced a false statement we will shade the region that does not contain the point. Also, note that the inequality is not strict. Therefore, the parabola will be solid.

Now, let's compare the correct graph with the given one.

We can see that the mistake Ron-Jon made was that he shaded the wrong region. By the way, you guessed right. Madame Christina is actually Ron-Jon's surprisingly sneaky math teacher.