In Problems 35-42, graph each system of inequalities. { y ≥ x^2-4 y ≤ x-2 .

Step 1: Graph the inequality u005C( y u005Cgeq x^2 u002D 4 u005C).u000Au002D This inequality represents the region above

In Problems 35-42, graph each system of inequalities. { ...

Key Concepts

Systems of Inequalities

A system of inequalities involves two or more inequality relations that must be satisfied simultaneously. The solution is found by graphing each inequality and identifying the region where all the individual solution sets overlap.

Graphing Quadratic Functions

Graphing quadratic functions entails plotting a parabola, which is a U-shaped curve that represents a second-degree polynomial. Key aspects include determining the vertex, axis of symmetry, and whether it opens upward or downward based on the coefficient of the squared term.

Graphing Linear Functions

Graphing linear functions involves drawing a straight line based on a linear equation. Important features include the slope (which indicates the steepness and direction of the line) and the y-intercept, which is the point where the line crosses the y-axis.

Shading Regions for Inequalities

When graphing inequalities, one shades the region of the graph that satisfies the inequality condition. For each individual inequality, the boundary (line or curve) is drawn and then the side corresponding to the solution of the inequality is shaded using a test point, typically the origin if it is not on the boundary.

Intersection of Regions

The final solution to a system of inequalities is the intersection of all shaded regions. This common area represents all the points that simultaneously satisfy every inequality in the system.

In Problems 35-42, graph each system of inequalities. $\left\{\begin{array}{l}y \geq x^2-4 \\ y \leq x-2\end{array}\right.$

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