## Yes, you are correct! The equation you provided, 2+3(x-2)+(x-2)^2, is the correct parabolization of the equation x^2-x at x=2.

To find the parabolization, you followed the correct steps:

1. Calculated c0 = f(a) = 2^2 - 2 = 2

2. Calculated c1 = f'(a) = 2(2)-1 = 3

3. Calculated c2 = f''(a)/2 = 2/2 = 1

Then, you used the formula P(x) = c0 + c1(x-a) + c2(x-a)^2 to substitute the values of c0, c1, and c2, which gave you the equation 2+3(x-2)+(x-2)^2.

To verify if the equation is correct, you can simplify it:

2+3(x-2)+(x-2)^2 = 2 + 3x - 6 + (x^2 - 4x + 4) = x^2 - x

As shown, the simplified equation matches the original equation x^2 - x, so your parabolization is indeed correct!