Chapter 1.9, Problem 25E

Solution

Graph the system of inequalities consisting of $y\ge x^2-3x-6\text{ and }y\ge 2x^2+7x+6$ .

Given:

The inequalities are $y\ge x^2-3x-6\text{ and }y\ge 2x^2+7x+6$ .

Graph:

The graph for the system of inequalities $y\ge x^2-3x-6\text{ and }y\ge 2x^2+7x+6$ is shown below.

  

Interpretation:

From the graph it can be interpreted that the graph for $y\ge x^2-3x-6$ is an upward parabola with the bold parabolic curve in green and the graph for $y\ge 2x^2+7x+6$ is also an upward parabola in blue with bold parabolic curve. Therefore, the common region representing the system of inequalities $y\ge x^2-3x-6\text{ and }y\ge 2x^2+7x+6$ is shown in graph.