Big Ideas Math Algebra 2, 2014
BI
Big Ideas Math Algebra 2, 2014 View details
6. Quadratic Inequalities
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Exercise 48 Page 146

Practice makes perfect
a A point is a solution of the system if it lies in the overlapped region. Since the parabolas are dashed, a point that is on any of the curves is not a solution. Let's arbitrarily plot two points in the overlapped area.

The points and lie in this region. Therefore, these points are solutions of the system. Note that and are only two of the infinitely many solutions.

b Let's plot the points and on the given coordinate plane.

Notice that both points lie on the parabolas. Since the parabolas are dashed, the solution set does not include points on the curves. Therefore, the points and are not solutions of the system.


c From Part B we know that the points and lie on the dashed parabolas and are not solutions of the system. Furthermore, note that the points lie on both curves. Therefore, if we want one of them, let's say to be a solution, we would have to make both parabolas solid.

Notice that now both points are solutions of the system. However, we only wanted one of them to be a solution. Therefore, it is not possible to change the inequality symbols to satisfy the required conditions.