Question

Describe how the graph of y= x2 can be transformed to the graph of the given equation.

y = (x-4)2-8



A Shift the graph of y = x2 right 4 units and then up 8 units.

B Shift the graph of y = x2 right 4 units and then down 8 units.

C Shift the graph of y = x2 left 4 units and then down 8 units.

D Shift the graph of y = x2 down 4 units and then left 8 units.

Answer 1

Starting with a function\[y=f(x)\]the graph of\[y=f(x-h)+k\]is the graph of \(f(x)\) shifted \(h\) units to the right and \(k\) units up

Answer 2

How do you make that into y = (x-4)2-8 i dont get how to get that from this equation

Answer 3

@TuringTest

Answer 4

you are given\[y=f(x)=x^2\]they want to know what is\[y=(x-4)^2-8=f(x-4)-8\]use the transformation rules I wrote to identify how the graph will change

Answer 5

So for something else im struggling with if you have one without parenthesis like y = x^2 + 13 how would you do that ?

Answer 6

what is \(h\) in this case?

Answer 7

I think the x^2?
@TuringTest

Answer 8

if your function is originally\[y=f(x)=x^2\]then\[y=f(x-h)=(x-h)^2\]i.e. \(f(x-h)\) means we replace all the x's with \(x-h\)
if something is added that does not \(change\) \(x\) that must be \(k\)
therefor in the transformation\[x^2\to x^2+13\]the x part does not change, so \(h=0\)
make sense?

Answer 9

so it would shift to the right 13 units ... right @TuringTest

Answer 10

Not quite
h is the part that moves the graph left and right
k moves it up and down
what is h?
what is k?

Answer 11

Im really guessing here but I now think that you have to Shift the graph of y = x2 up 13 units.

Answer 12

well you guessed right :)

Answer 13

h=0
k=13
so up 13 units, yes

Answer 14

Thank you

Answer 15

welcome!