Chapter 1.9, Problem 20E

Solution

Graph the system of inequalities consisting of $y\ge 2x^2\text{ and }y<-x^2+1$ .

Given:

The inequalities are $y\ge 2x^2\text{ and }y<-x^2+1$ .

Graph:

The graph for the system of inequalities $y\ge 2x^2\text{ and }y<-x^2+1$ is shown below.

  

Interpretation:

From the graph it can be interpreted that the graph for $y\ge 2x^2$ is an upward parabola including the bold parabolic curve in green and the graph for $y<-x^2+1$ is a downward parabola with dotted parabolic curve. Therefore, the common region representing the system of inequalities $y\ge x^2\text{ and }y<-x^2+5$ is shown in graph.