work out x^2-6x+8 as a(x-h)^2+k?

Answer 1

This problem involves the "completing the square" method.
First set the polynomial equal to zero.
x ^ 2 - 6x + 8 = 0.
Then we separate complete the square.
x ^ 2 - 6x + 9 + 8 = 0 + 9.
We take half of -6 which is -3 and square which is 9. Then we had to add 9 to both sides of the equation.
Now we factor x ^ 2 - 6x + 9.
( x ^ 2 - 6x + 9 ) + 8 = 0 + 9
( x - 3 ) ^2 - 1 which is in the form a(x-h)^2+k.
Note that a = 1.

Answer 2

x² - 6x + 8 = (x² - 6x + 9) - 9 + 8 = (x - 3)² - 1
Where h = 3 and k = -1