Question

Graph y < x^2 + 2. Click on the graph until the correct one appears.

Answer 1

Where is the graph Trexfify1

Answer 2

The graph of given inequality is attached below.

Explanation:

The given inequality is

`y<x^2+2`

The related equation of the of the given inequality is

`y=x^2+2` .... (1)

The related curve is dotted because the sign of inequality is <. The points on the curve are not included in the solution set.

It is a quadratic equation. So, the graph of related equation is a parabola.

The vertex form of a parabola is

`y=(x-h)^2+k` .... (2)

From (1) and (2), we get

`h=0,k=2`

The vertex of the parabola is at (0,2).

At x=1,

`y=(1)^2+2=3`

At x=-1,

`y=(-1)^2+2=3`

It means the graph if passing through (1,3) and (-1,3).

Check the inequality by (0,0),

`(0)<(0)^2+2`

`0<2`

This statement is true, it means (0,0) is in the shaded region.

The graph of given inequality is attached below.