Q. 45 - Precalculus Enhanced with Graphing Utilities

Question

In Problems 44 and 45, graph each inequality by hand. Verify your results using a graphing utility.

$y\le x^2$

Step-by-Step Solution

Answer

The graph of $y\le x^2$is 

Step 1. Given data

The given inequality is 

$y\le x^2$

Step 2. Properties of the graph of the inequality

Graph of $y=x^2$ will be a line

now test a point $(3,4)$for inequality

$$\begin{gathered} y\le x^2 \\ 4\le 3^2 \\ 4\le 9 \end{gathered}$$

inequality satisfied so the point  will lie in the region of inequality

So shade the region from parabola toward point $(3,4)$ 

Step 3. graph of the inequality

Plot a parabola $y=x^2$of a solid line and shade the region outside the parabola to plot the graph of $y\le x^2$

Step 4. Verification

Plot the graph of $y\le x^2$using a graphing utility

Graph matches with our graph so our graph is correct.