Graphing Square Root Inequalities

Graphing Square Root Inequalities

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

Example 1: Graph y > -√x + 3

Graph the given inequality. y > -Square root [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

Graph the given inequality. y <= Square root [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.