Graph y = √x - 2 from y = √x

Step by step

The question

Question: graph y = √x − 2 from y = √x.

We know the graph of y = √x.

It is half a U, lying on its side.

1 Read the changes

Outside, at the end, − 2 takes 2 away from every y.

So the graph moves down 2.

2 Start from y = √x

Draw the grid.

Draw y = √x first.

It goes through (0, 0), (1, 1) and (4, 2).

3 Move the points

The start point (0, 0) moves down 2.

(0, 0) goes to (0, −2).

(1, 1) goes to (1, −1).

(4, 2) goes to (4, 0).

4 Draw the new graph

Join the new points with the same shape.

This is y = √x − 2.

5 Check

Let's check.

Put x = 0 in the new rule.

We get y = −2: the point (0, −2) we drew.

And x = 4 gives y = 0: the point (4, 0).

Let's look back.

First: read the changes.

Then: start from y = √x.

Then: move the points.

Then: draw the new graph.

Last: check.