Step by step
The question
Question: graph y = one third times x², from y = x².
We know the graph of y = x².
It is a U.
1 Read the changes
The one third in front makes every y one third as big.
Smaller y's: the graph gets wider and flatter.
Careful!
A number bigger than 1 makes it narrower.
A number between 0 and 1 makes it wider.
2 Start from y = x²
Draw the grid.
Draw y = x² first.
It goes through (−3, 9), (0, 0) and (3, 9).
3 Shrink the y's
(−3, 9): one third of 9 is 3.
It goes to (−3, 3).
(0, 0) stays: one third of 0 is 0.
(3, 9): one third of 9 is 3.
It goes to (3, 3).
4 Draw the new graph
Join them with the same shape, wider.
This is the new graph.
5 Check
Let's check: put x = 3 in the new rule.
One third of 9 is 3.
We get the point (3, 3).
It works!
Let's look back.
First: read the changes.
Then: start from y = x².
Then: shrink the y's.
Then: draw the new graph.
Last: check.