Answer:
y = (x -3)^2 -1
Explanation:
You want the equation y = x^2 -6x +8 written in vertex form: y = (x -h)^2 +k.
Expansion
Expand the vertex form and you get ...
(x -h)^2 +k = x^2 -2hx +h^2 +k
Coefficients
Matching coefficients to the given equation, you have ...
x^2 coefficient: 1 = 1
x coefficient: -6 = -2h ⇒ h = 3
constant: 8 = h^2 +k = 9 +k ⇒ k = -1
Vertex form
Using the values of h and k in the given form, your equation is ...
y = (x -3)^2 -1
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Additional comment
We often do this by grouping the x-terms, factoring out the leading coefficient if it is not 1.
(x^2 -6x) +8
Now, we locate the x-coefficient (-6) and divide it by 2. This value is then squared.
(-6/2)^2 = 9
This square is added inside parentheses, and an equivalent value is subtracted outside parentheses. (The "equivalent value" will be 9 multiplied the leading coefficient.)
(x^2 -6x +9) +8 -9
You see this simplifies to the equation we show above:
y = (x -3)^2 -1