SOLUTION: if x^2-5x+6=(x-h)^2+k what is the value of k?

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Question 945050: if x^2-5x+6=(x-h)^2+k what is the value of k?
Found 2 solutions by josgarithmetic, MathTherapy:
Answer by josgarithmetic(39617) About Me  (Show Source):
You can put this solution on YOUR website!
Difficult to understand through viewing the two expressions. COMPLETE The SQUARE to transform the left member into standard form, and then you can identify k by corresponding position.

See your lesson on completing the square so you know why the term to use for this will be %285%2F2%29%5E2=25%2F4.

x%5E2-5x%2B%285%2F2%29%5E2%2B6-%285%2F2%29%5E2
%28x-5%2F2%29%5E2%2B6-25%2F4
%28x-5%2F2%29%5E2%2B24%2F4-25%2F4
%28x-5%2F2%29%5E2-1%2F4=%28x-h%29%5E2%2Bk


highlight%28k=-1%2F4%29

Answer by MathTherapy(10552) About Me  (Show Source):
You can put this solution on YOUR website!

if x^2-5x+6=(x-h)^2+k what is the value of k?


y+=+x%5E2+-+5x+%2B+6

h, or x = -+-+5%2F%282+%2A+1%29, or 5%2F2

k, or y = %285%2F2%29%5E2+-+5%285%2F2%29+%2B+6 -------- Substituting 5%2F2 for h, or x

k, or y = 25%2F4+-+25%2F2+%2B+6

k, or y = 25%2F4+-+50%2F4+%2B+24%2F4

k, or highlight_green%28y+=+%28-+1%29%2F4%29%29