Question

For the inequality y+4x≤x2+2, where is the graph shaded and is the curve solid or dotted?

Answer 1

The graph shaded outside the parabola and the curve is solid.

Explanation:

The given inequality is

`y+4x\leq x^2+2`

It can be rewritten as

`y\leq x^2-4x+2`

The sign of inequality is
`\leq`, so the curve is a solid line.

The related equation of line is

`y=x^2-4x+2`

Table of values is

x 0 2 4

y 2 -2 2

Plot these points and draw a U-shaped curve.

Check the equality for (0,0).

`0\leq (0)^2-4(0)+2`

`0\leq 2`

This statement is true. So, (0,0) lies in the shaded portion.

So, shade the graph outside the parabola.