Chapter 1.9, Problem 14E

Solution

Graph the quadratic inequality $y\ge -2x^2+9x-4$ .

The solution for the quadratic inequality is $x\in \left(-\infty ,0.5\right]\cup \left[4,\infty \right)$ .

Given:

The quadratic inequality is $y\ge -2x^2+9x-4$ .

Graph:

The graph for the quadratic inequality $y\ge -2x^2+9x-4$ is shown below.

  

Interpretation:

From the graph it can be interpreted that the graph is a downward parabola with $x-$ intercepts $\left(0.5,0\right)\text{ and }\left(4,0\right)$ . And the shaded region lies outside the parabolic region including the bold parabolic curve. Therefore, the solution for the inequality $y\ge -2x^2+9x-4$ is all point lying outside the shaded region including the dark parabolic curve.

Hence, the solution for the quadratic inequality is $x\in \left(-\infty ,0.5\right]\cup \left[4,\infty \right)$ .