{{ item.displayTitle }}

No history yet!

Student

Teacher

{{ item.displayTitle }}

{{ item.subject.displayTitle }}

{{ searchError }}

{{ courseTrack.displayTitle }} {{ printedBook.courseTrack.name }} {{ printedBook.name }}

A quadratic inequality is an inequality involving a quadratic relation in one or two variables. For example, $y\geq 3x^2-2x-4,$

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. $(\text{-} 3, \text{-} 4), \quad (1,2), \quad \text{ and } \quad (3,7)$

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, $\begin{aligned} &(\text{-} 3,\text{-} 4) && \text{is not a solution, but } \\ &(1,2) && \text{is a solution.} \end{aligned}$ 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 $\begin{aligned} &(3,7) && \text{is not a solution.} \end{aligned}$

{{ 'mldesktop-placeholder-grade' | message }} {{ article.displayTitle }}!

{{ exercise.headTitle }}

{{ 'ml-heading-exercise' | message }} {{ focusmode.exercise.exerciseName }}