The value of k is [tex]-h^2 -2xh -5x + 6[/tex]
Given;
x^(2)-5x+6=(x+h)^(2)+k
Expand the expression on the right side, we have
[tex]x^2 - 5x + 6 = (x+ h) (x+ h) + k[/tex]
[tex]x^2 -5x + 6 = x^2 +xh + xh + h^2 +k[/tex]
Collect like terms
[tex]x^2 -5x + 6 = x^2 + 2xh + h^2 + k[/tex]
[tex]x^2 -5x + 6 -x^2 - 2xh -h^2 = k[/tex]
We then have
[tex]-5x + 6 -2xh -h^2 = k[/tex]
[tex]k = -h^2 -2xh -5x + 6[/tex]
Thus, we have k as [tex]-h^2 -2xh -5x + 6[/tex]
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