Question

Which phrase best descubes the translation from the graph y = (x - 5)2 + 7 to the graph of y = (x + 1)2 - 2?

6 units left and 9 units down
6 units nght and 9 units down
6 units left and 9 units up
6 units right and 9 units up

Answer 1

"6 units left and 9 units down"

Explanation:

Suppose a function is given in this form:

`y=(x-a)^2+b`

This is the parent function y = x^2

• translated a units right (left if there was a + before a)
• translated b units up (down if there was a - before b)

Now, to go from
`y=(x-5)^2+7` to
`y= (x+1)^2-2` , we can see that:

• first function is 5 units right and 2nd one is 1 unit left, so there is a horizontal translation of 6 units left
• first function is 7 units above and 2nd one is 2 units down, so there is a vertical translation of 9 units down

Thus, "6 units left and 9 units down" is the transformation(translation).