SOLUTION: I don't know exactly how to get this form y=a(x-h)^2+k from the function y=x^2-6x+8. I don't know how to get this function into this particular form.

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Question 76541: I don't know exactly how to get this form y=a(x-h)^2+k from the function y=x^2-6x+8. I don't know how to get this function into this particular form.
Found 2 solutions by scott8148, Earlsdon:
Answer by scott8148(6628) (Show Source):
You can put this solution on YOUR website!
a little factoring and regrouping will illuminate your answer

y=x^2-6x+8 may be rewritten as y=1(x^2-6x)+8..."completing the square" gives y=1(x^2-6x+9)+8-9...the +9 added inside the parentheses is "compensated" by the -9 added outside

note that if the coefficient of the x^2 term is something besides 1, the "compensation" is affected accordingly

factoring and consolidating terms gives y=1(x-3)^2-1...so a=1, h=3 and k=-1

Answer by Earlsdon(6294) (Show Source):
You can put this solution on YOUR website!
Convert:
to:
from.
Use the process known as "completing the square"
You want to make the constant term here equal to the square of half the x-coefficient (that's the -6).

So you must add a 1 to the 8 to make the required 9. But to keep the same equation, you must also subtract 1 to compensate for the added 1.
Now rearrange this as follows:
Factor the parentheses.
...and there you have it! Compare with:

Here: a = 1, h = 5, and k = -1