Question

In Problems 35-42, graph each system of inequalities. $\left\{\begin{array}{l}x^2+y^2 \leq 25 \\ y \leq x^2-5\end{array}\right.$ 

   In Problems 35-42, graph each system of inequalities.
$\left\{\begin{array}{l}x^2+y^2 \leq 25 \\ y \leq x^2-5\end{array}\right.$
Precalculus: pearson new international edition
Precalculus: pearson new international edition
Michael Sullivan 9th Edition
Chapter 11, Problem 40 ↓

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The system of inequalities consists of two parts:  Show more…

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In Problems 35-42, graph each system of inequalities. $\left\{\begin{array}{l}x^2+y^2 \leq 25 \\ y \leq x^2-5\end{array}\right.$
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Key Concepts

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Systems of Inequalities
This concept involves finding and graphing the regions that satisfy multiple inequalities at the same time. It requires plotting each inequality on the coordinate plane and then identifying the overlapping area where all conditions are met simultaneously.
Circle Equation and Inequality
A circle in the Cartesian plane is defined by an equation of the form x² + y² = r². When the equation is given as an inequality, such as x² + y² ? r², it represents all the points inside the circle and on the boundary, which is an essential idea for understanding regions defined by quadratic constraints.
Parabolic Equation and Inequality
A parabola is represented by a quadratic equation like y = ax² + bx + c. When dealing with an inequality, for example y ? ax² + bx + c, it indicates that the graph includes all points below (or on, depending on the inequality sign) the parabola. This concept is key to visualizing and determining the solution set of quadratic inequalities.
Intersection of Graphical Regions
In problems that involve multiple inequalities, the solution is found where the regions defined by each individual inequality overlap. This concept is crucial because it combines the graphs of our inequalities into one cohesive diagram that represents the simultaneous solutions of the system.
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In Problems $35-42,$ graph each system of inequalities. $\left\{\begin{aligned} x y & \geq 4 \\ y & \geq x^{2}+1 \end{aligned}\right.$
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