The coordinates of a few points are (1,1), (2,4), (3,9) and (4,16). The first part of the problem says to first stretch the vertical (y) component by doubling it, so the point pairs become

1,2

2,8

3,18

4,32

Remember, we’re not shifting left to right, so the x values remain the same.

How can you change the equation to get that result? You should be able to figure it out easily with the examples in front of you, right?

Now you want to shift everything up by one unit, so the point pairs are now

1,3

2.9

3,19

4,33

What do you have to do to the equation to make every point change like that?

b) Let’s do the same thing in the reverse order. The point pairs shifted upward one unit become

1,2

2,5

3,10

4,17

How do you change the original equation to get those points?

Then do the stretching. That makes the points

1,4

2,10

3,20

4.34

Again, the x values of the points aren’t affected — only the vertical (y) values. How do you get that result?

c) The graphs won’t be the same. If your allowance is $10 and I first double it and then add a dollar, the new allowance will be 10*2+1 or $21. If I increase it by a dollar and then double it, it will be $22. The second number is bigger because I’m doubling a larger number — in this equation I’m adding 1 first and then doubling the result. In the first instance, I added the 1 after I doubled the y value.

The first equation, if you haven’t gotten it, is y=2x^2+1. The second equation is y=2(x^2+1), or y=2x^2+2. You can see there that you wind up adding 2 instead of 1 in each case.