write in form y=a(x-h)^2+k

y=x^2-x-9
(x^2-2x)-9
complete the square
(x^2+2x+1-1)-9
(x^2+2x+1)-1-9
(x+1)^2-9

-1 - 9 = -10

also your -2x mysteriously turned into +2x

so

(x-1)^2 - 10

y= x^2 -x - 9

y=(x^2 -x + 0.5^2 - 0.5^2) -9 ; we get 0.5 by dividing 1 by 2)
y=(x^2 -x + 0.25) - 0.25 -9
y=(x-0.5)^2 - 9.25

roro is correct, I misread your question

To express the equation y = x^2 - x - 9 in the form y = a(x-h)^2 + k, we need to complete the square.

Step 1: Group the x^2 and x terms together, and leave the constant term separate:
y = (x^2 - x) - 9

Step 2: Complete the square by adding and subtracting [(coefficient of the x term) / 2]^2 inside the parentheses:
y = (x^2 - x + 1^2) - 1 - 9

Step 3: Simplify the terms inside the parentheses:
y = (x^2 - x + 1) - 10

Step 4: Factor the quadratic term inside the parentheses, if possible:
y = (x - 1/2)^2 - 10

Finally, we can rewrite the equation y = x^2 - x - 9 in the form y = a(x-h)^2 + k as y = (x - 1/2)^2 - 10.