SOLUTION: For the function y= x2 - 6x + 8, put the function in the form y = a (x - h) squared + k. I was able to solve it by factoring and using the quadratic formula, but I can't figure out

Question 77475: For the function y= x2 - 6x + 8, put the function in the form y = a (x - h) squared + k. I was able to solve it by factoring and using the quadratic formula, but I can't figure out how to use this formula.
Answer by jim_thompson5910(35256) (Show Source): You can put this solution on YOUR website!

Solved by pluggable solver: Completing the Square to Get a Quadratic into Vertex Form

Start with the given equation

Subtract from both sides

Factor out the leading coefficient

Take half of the x coefficient to get (ie ).

Now square to get (ie )

Now add and subtract this value inside the parenthesis. Doing both the addition and subtraction of does not change the equation

Now factor to get

Distribute

Multiply

Now add to both sides to isolate y

Combine like terms

Now the quadratic is in vertex form where , , and . Remember (h,k) is the vertex and "a" is the stretch/compression factor.

Check:

Notice if we graph the original equation we get:

Graph of . Notice how the vertex is (,).

Notice if we graph the final equation we get:

Graph of . Notice how the vertex is also (,).

So if these two equations were graphed on the same coordinate plane, one would overlap another perfectly. So this visually verifies our answer.

So the quadratic can be converted to the standard form which is
where a=1, h=3, and k=-1
Now we let y=0

Add 1 to both sides

Which means

or
Now add 3 to both sides for each case to solve for x:
So our solutions are
or
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