Chapter 7.5, Problem 39E

To determine

To sketch: the graph of the solution set of the system of inequalities

  $\{\begin{array}{l}{x}^2+y\le 7\\ x\ge -2\\ y\ge 0\end{array}$

Explanation of Solution

Given information : The system of inequalities

  $\{\begin{array}{l}{x}^2+y\le 7\text{ Inequality 1}\\ x\ge -2\text{ Inequality 2}\\ y\ge 0\text{ Inequality 3}\end{array}$

Graph :

  

Interpretation :

Find the points of intersection of each pair of equations.

Vertex A:

From Inequality 1 and Inequality 2,

  $x^2+y=7$ , $x=-2$

  $4+y=7$

  $y=3$

  $A=(-2,3)$

Vertex B:

From Inequality 1 and Inequality 3,

  $x^2+y=7$ , $y=0$

  $x^2=7$

  $x=\pm \sqrt{7}$

Inequality 2 $\Rightarrow$ Only values $x\ge -2$ need to be considered.

So, $x=-\sqrt{7}=-2.6$ can be omitted.

  $x=\sqrt{7}$

  $\text{B}=(\sqrt{7},0)$

Vertex C:

From Inequality 2 and Inequality 3,

  $x=-2$ , $y=0$

  $\text{C}=(-2,0)$