Step by step
The question
Question: graph y = (x − 2)² from y = x².
We know the graph of y = x².
It is a U, with its turning point at (0, 0).
1 Read the changes
Inside, next to x, we have − 2.
x = 2 makes the inside 0.
So the turning point moves to x = 2: right 2.
Careful!
Inside, it goes the opposite way to the sign.
2 Start from y = x²
Draw the grid.
The x-axis goes across.
The y-axis goes up and down.
They meet at 0.
That point is called the origin.
Draw y = x² first.
Its turning point is at (0, 0).
3 Move the turning point
Move it right 2.
The new turning point is (2, 0).
4 Draw the new graph
The shape stays the same.
From the turning point, 1 right, 1 up.
And 1 left, 1 up.
Join them with the same U.
This is y = (x − 2)².
5 Check
Let's check.
Put x = 2 in the new rule.
We get y = 0: the turning point (2, 0).
And x = 3 gives y = 1: the point (3, 1) we drew.
Let's look back.
First: read the changes.
Then: start from y = x².
Then: move the turning point.
Then: draw the new graph.
Last: check.