Big Ideas Math Algebra 2, 2014
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Big Ideas Math Algebra 2, 2014 View details
6. Quadratic Inequalities
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Exercise 24 Page 144

Remember that if the inequality is not strict, then the related parabola is a solid line.

Practice makes perfect
We want to solve the given system of inequalities by graphing. Note that both inequalities of the system are quadratic inequalities.
Let's graph each of them, one at a time.

Inequality I

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 shade the region that contains the point. If not, we shade the opposite region.

Let's draw the graph of the related function, which is

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

Inequality II

We will follow the same three steps as before. Let's draw the graph of the related function, which is

Next, let's determine which region to shade by testing a point. We will use as our test point.

Inequality Test Point Statement Is It the Good Region?
Yes

Let's graph it!

Final Solution Set

The solution set is the overlapping region.