In Problems 35-42, graph each system of inequalities. { x^2+y^2 ≤ 16 y ≥ x^2-4 .

Step 1: Understand the inequalities.u000AThe first inequality u005C(x^2 + y^2 u005Cleq 16u005C) represents the r

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

Key Concepts

Graphing Inequalities

Graphing inequalities involves plotting the boundary curves or lines defined by the corresponding equality, and then determining which side of the boundary satisfies the inequality. This process often includes using test points to identify the region of the plane that represents solutions to the inequality while considering whether the boundary is included based on the inequality symbol.

Circle Inequality

A circle inequality such as one derived from a quadratic expression in x and y represents a circular region. The equality defines the circle's boundary (with a specific center and radius), while the inequality indicates whether the interior, the exterior, or the boundary itself is part of the solution set.

Parabolic Inequality

A parabolic inequality involves a quadratic function in one variable expressed in terms of the other, representing a parabolic curve. The equality gives the curve's shape and orientation, and the inequality specifies the region above or below this parabola that satisfies the condition.

Systems of Inequalities

Systems of inequalities require that multiple inequalities be satisfied simultaneously. The solution is found by graphing each inequality and then determining the intersection of all the individual solution regions, which represents the set of points that satisfy every condition in the system.

In Problems 35-42, graph each system of inequalities. $\left\{\begin{array}{l}x^2+y^2 \leq 16 \\ y \geq x^2-4\end{array}\right.$

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