Chapter 1.9, Problem 2GP

Solution

Graph the inequality $y\le 2x^2-3x+1$ .

Given:

The inequality is $y\le 2x^2-3x+1$ .

Graph:

The graph for the inequality $y\le 2x^2-3x+1$ is shown below.

  

Interpretation:

From the graph it can be interpreted that the graph is an upward parabola with $x-$ intercepts $\left(0.5,0\right)\text{ and }\left(1,0\right)$ . And the shaded region lies outside the parabolic region which includes the bold parabolic curve. Therefore, the solution for the inequality $y\le 2x^2-3x+1$ is all point lying outside the shaded region including the dark parabolic curve. Hence, the solution for the inequality is written as $x\in \left(-\infty ,0.5\right]\cup \left[1,\infty \right)$ .