We will graph the given quadratic inequality $y \geq x^{2} + 2,$ then we will find the error. To graph the quadratic inequality, we will follow three steps.

Graph the related quadratic function.
Test a point not on the parabola.
Shade accordingly. If the point satisfies the inequality, we shade the region that contains the point. If not, we shade the opposite region.

Step $1$

Let's draw the graph of the related function, which is $y = x^{2} + 2 .$

Step $2$

Next, let's determine which region to shade by testing a point. For simplicity, we will use

(0, 0)

as our test point. Let's see if it satisfies the given inequality.

y \geq x^{2} + 2

SubstituteII

$x = 0$ , $y = 0$

0 \geq ? (0)^{2} + 2

CalcPow

Calculate power

0 \geq ? 0 + 2

AddTerms

Add terms

0 ≱ 2 \times

Step $3$

Since $(0, 0)$ produced a false statement, we will shade the region that does not contain the point. Also, note that the inequality is not strict. Therefore, the parabola will be solid.

Now, let's compare the correct graph with the given one.

We can see that there is only one mistake: in the given graph the parabola is dashed.

Step 1

Step 2

Step 3

Step $1$

Step $2$

Step $3$

Exercise