Question

Describe the translation of the graph of y = x^2 that results in the graph of y = (x - 3)^2.


left 3 units
right 3 units
down 3 units
up 3 units

Answer 1

I think it's C. down 3 units. Am I right?

Answer 2

you shift up or down by adding a number (call it k), like this
\[ y = x^2 + k\]
to move the graph sideways you shift by h this way
\[ y = (x-h)^2 \]
the trick part is which way , left or right?

Answer 3

It'd be left, I think. Because the negative numbers are on the left, and the minus/negative sign would shift it left? I think.......

Answer 4

@phi

Answer 5

sorry for the long delay. For the y shift (up and down) it works they way you think. +k means shift up k steps and -k means down k steps

but for the sideways shift , it works *backwards* (gack!)
so y=(x-3)^2 shifts the graph y= x^2 three steps to the *right*