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QUESTION: A horizontal translation is applied to the graph of y= X^ 3 + 2 so that it will pass through (3, 10) what is the new equation for the graph?

y=(x+a) ^3+ 2
10= (3+ a) ^3 + 2
10-2= (3+ a) ^3 + 2-2
8= (3+ a) ^3
Take the cube root of each side...
2= 3-a solve for a
So I went like this:
2-2+a= 3-a-2+a
a= 1

So the new equation would be? I am unsure which equation do I put it in for?

8= (3+ a) ^3
Take the cube root of each side...
2= 3-a solve for a ****Nope, you changed the sign on a. 1=3+a, a=-1

The new equation is

y=(x-1)^3 +2 This shifts the equation along the horizontal axis to the right.

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