SOLUTION: Write the function in vertex form. y=x^2-3x+6

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Question 778461: Write the function in vertex form.
y=x^2-3x+6

Answer by Edwin McCravy(20054) About Me  (Show Source):
You can put this solution on YOUR website!
We want to get y = a(x-h)²+k 

y = x²-3x+6 in the form 

Put brackets around the first two terms on the
right,

y = [x²-3x]+6

 and since the coefficient of x² is 1 put 1
in front of the parentheses. Normally you
would factor out the coefficient of x²:

y = 1[x²-3x]+6

We complete the square inside the brackets:

1. Multiply the coefficient of x, which is -3
   by 1%2F2, getting -3%2F2.
2. Square -3%2F2 getting %28-3%2F2%29%5E2 = 9%2F4
3. Add %22%22%2B9%2F4-9%2F4, which is really 0, inside the
   brackets:

y = 1[x²-3x+9%2F4-9%2F4]+6

Factor the first three terms inside the bracket like this
             x²-3x+9%2F4 = (x-3%2F2)(x-3%2F2) = (x-3%2F2)²

y = 1[(x-3%2F2)²-9%2F4]+6

Remove the bracket

y = 1(x-3%2F2)²-9%2F4+6 

Write the 6 as 24%2F4

y = 1(x-3%2F2)²-9%2F4+24%2F4

y = 1(x-3%2F4)²+15%2F4 

y = a(x-h)²+k

The vertex is (h,k) = (3%2F4,15%2F4)

Edwin