Question

Which function represents a translation of the graph of y=x^2 by 8 units to the right?

A. y=(x+8)^2
B. y=x^2+8
C. y=(x-8)^2
D. y=8x^2

Answer 1

Do you have an idea already? Or are you not sure how to figure it out?

Answer 2

i think its b but i wanted some outside confirmation feel me?

Answer 3

Sure. It's not b.

Answer 4

welll then i have no idea

Answer 5

In general, lets say you are looking at translations of a function:

y = x^2

The translations will be of the form:

y-k = (x-h)^2

You can add k to both sides so it might look more like:

y = (x-h)^2 + k

But in anycase, the h represents a shift in the left/right direction, the k is a shift up and down.

Answer 6

So with that in mind, do you have another guess?

Answer 7

oh i see so the answer should be c?

Answer 8

oh i see so the answer should be c?

Answer 9

oh i see so the answer should be c?

Answer 10

oh i see so the answer should be c?

Answer 11

f(x) = x^2 f(x) = x^2 + 8 <---that shifts the function up 8 units on the graph
f(x) = x^2 - 8 <----that shifts the function down 8 units on the graph
Shifting right or left is a little more tricky, because you have to directly modify the function's variable.
For example:
f(x) = x^2 f(x+8) = (x+8)^2 <----that will shift the graph 8 points to the left (its inverse for horizontal translation, positive = to the left negative = to the right)
f(x-8) = (x-8)^2 <----that will shift the graph 8 points to the right

Answer 12

oh i see so the answer should be c?

Answer 13

That's correct.

Answer 14

If it were y=(x+8)^2 it would be a shift of 8 to the left instead of the right because it's y=(x-(-8))^2