Chapter 1, Problem 43REAE

Solution

Solve the inequality $-x^2+4x+3\ge 0$ by graphing it.

The solution of the inequality is $-0.646\le x\le 4.646$ .

Given:

The inequality is $-x^2+4x+3\ge 0$ .

Graph:

The graph for the inequality $-x^2+4x+3\ge 0$ is shown below.

Make the sketch for the parabola $y=-x^2+4x+3$ and use bold lines for the graph because the inequality sign is $\left(\ge \right)$ in the inequality $-x^2+4x+3\ge 0$ .

  

Interpretation:

From the graph it can be interpreted that the graph is a downward parabola with $x-$ intercepts $\left(-0.646,0\right)\text{ and }\left(\text{4}\text{.646},0\right)$ included in the solution of inequality because of $\left(\ge \right)$ sign in inequality. Therefore, the solution for the inequality $-x^2+4x+3\ge 0$ is all points lying in the shaded region for which the inequality satisfies the condition $-x^2+4x+3\ge 0$ .

Hence, the solution for the inequality is $-0.646\le x\le 4.646$ .