Chapter 3, Problem 9CT

To determine

To calculate: The solution of the system of equations or inequalities.

Answer to Problem 9CT

The required solutions are $\left(-4.233,2.48\right)$ and $\left(-0.567,-1.92\right)$ .

Explanation of Solution

Given information:

The system of inequalities: $y\ge \frac{1}{4}{x}^2-2$

  $y<-{\left(x+3\right)}^2+4$

Calculation:

The given system of inequalities is,

  $y\ge \frac{1}{4}{x}^2-2$........................... (1)

  $y<-{\left(x+3\right)}^2+4$........................... (2)

To find the solutions of the given two inequalities, draw the graphs of the inequalities.

The graphs of inequalities (1) and (2) are shown below:

  

In the above graph, the two inequalities intersect each other at the points $\left(-4.233,2.48\right)$ and $\left(-0.567,-1.92\right)$ .

Hence, the required solutions are $\left(-4.233,2.48\right)$ and $\left(-0.567,-1.92\right)$ .