# Graphing Square Root Inequalities

How to graph square root inequalities on a coordinate plane: examples and their solutions.

## Example 1: Graph *y* > -√*x* + 3

First draw [*y* = -√*x* + 3].

The inequality sign doesn't include [=].

So use a dashed line.

The starting point is (0, 3).

So draw an empty point on (0, 3).

The coefficient of the square root is (-).

The coefficient of *x* is 1: (+).

So the graph

[decreases] to the [right]

smoother and smoother.

Graphing square root functions

*y* > -√*x* + 3

This shows that*y* is greater than the right side.

So color the upper region of the dashed line.

This graph is the answer.

## Example 2: Graph *y* ≤ √*x* + 1 - 2

Find the starting point of the graph.*x* + 1 = *x* - (-1)

So the starting point is (-1, -2).

Draw [*y* = √*x* - (-1) - 2].

The inequality sign does include [=].

So use a solid line.

The starting point is (-1, 2).

So draw a full point on (-1, -2).

The coefficient of the square root is (+).

The coefficient of *x* is 1: (+).

So the graph

[increases] to the [right]

smoother and smoother.

*y* ≤ √*x* - (-1) - 2

This shows that*y* is less than (or equal to) the right side.

So color the lower region of the solid line.

This graph is the answer.