Step by step
The question
Question: graph y = one half times x², from y = x².
y = 12x2
We know the graph of y = x².
It is a U.
we know: y = x²
1 Read the changes
The one half in front makes every y one half as big.
Smaller y's: the graph gets wider and flatter.
12 in front → every y × 12
Careful!
A number bigger than 1 makes it narrower.
A number between 0 and 1 makes it wider.
Careful: a number between 0 and 1 in front: wider, not narrower
2 Start from y = x²
Draw the grid.
Draw y = x² first.
It goes through (−2, 4), (0, 0) and (2, 4).
3 Shrink the y's
(−2, 4): one half of 4 is 2.
It goes to (−2, 2).
(0, 0) stays: one half of 0 is 0.
(2, 4): one half of 4 is 2.
It goes to (2, 2).
4 Draw the new graph
Join them with the same shape, wider.
This is the new graph.
5 Check
Let's check: put x = 2 in the new rule.
One half of 4 is 2.
We get the point (2, 2).
It works!
x = 2: y = 12(2)2 = 12 × 4 = 2
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.
Answer
12 in front → every y × 12