Chapter 10, Problem 9CA

To determine

To write: The inequalities equation of parabola of the graph.

Answer to Problem 9CA

  $\mathrm{y}<-{\mathrm{x}}^2+2\mathrm{x}+4$ and $\mathrm{y}\ge {\mathrm{x}}^2-\mathrm{x}-6$ .

Explanation of Solution

Given: The graph given below,

  

There are two equation of parabola. One upward and one downward.

First find the equation of downward parabola. This is dotted line.

Equation of parabola: $\mathrm{y}<-{\mathrm{x}}^2+2\mathrm{x}+4$

One parabola upward and y-intercept $\left(0,-6\right)$ . The line solid.

  $\mathrm{y}\ge {\mathrm{x}}^2-\mathrm{x}-6$

Hence, the system of inequalities are $\mathrm{y}<-{\mathrm{x}}^2+2\mathrm{x}+4$ and $\mathrm{y}\ge {\mathrm{x}}^2-\mathrm{x}-6$ .