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{{ printedBook.courseTrack.name }} {{ printedBook.name }} A quadratic inequality is an inequality involving a quadratic relation in one or two variables. For example, $y≥3x_{2}−2x−4,$

is a quadratic inequaliy. Similar to linear inequalities, the solution set to a quadratic inequality is an entire region of the coordinate plane. However, instead of the boundary being a line, it is a parabola.Graphing a quadratic inequality is similar to graphing a quadratic function, but instead of a parabola, the graph is an entire region.

To graph the quadratic inequality $y<x_{2}+2x−1,$ draw the boundary, determine if the solution set lies inside or outside the parabola, and shade the region that contains the solution set.Graph the boundary

Test a point

Shade the appropriate region

If the test point is a solution to the inequality, the region in which it lies contains the entire solution set. If not, the other region represents the solution set. Here, the test point is $(0,0).$

The region containing $(0,0)$ is inside the parabola. Since $(0,0)$ is **not** a solution, the region **outside** the parabola containts the solution set.

Use the graph to determine if the following points are solutions to the corresponding inequality graphed in the coordinate system. Justify your answer. $(-3,-4),(1,2),and(3,7)$

Show Solution

The graph shows the solution set to the inequality. Let us begin by marking the three points on the coordinate plane.

A point that lies within the shaded region is a solution to the inequality, while a point that lies outside is not. Therefore, $ (-3,-4)(1,2) is not a solution,butis a solution. $ The point $(3,7)$ lies on the boundary. However, since the curve is dashed, points on the boundary are not included in the solution set. Therefore, the point $ (3,7) is not a solution. $

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