To convert the quadratic expression 6x - x^2 - 3 to the form of a(x - h)^2 + k by completing the square, follow these steps:
1. Rearrange the expression by grouping the x-terms together:
-x^2 + 6x - 3
2. Factor out the coefficient of the x^2 term, which is -1:
-(x^2 - 6x) - 3
3. To complete the square, take half of the coefficient of the x-term (6/2 = 3) and square it (3^2 = 9).
4. Add and subtract this value inside the parentheses:
-(x^2 - 6x + 9 - 9) - 3
5. Rearrange the terms within the parentheses:
-(x^2 - 6x + 9) - 3
6. Simplify the expression within the parentheses:
-(x - 3)^2 - 3
Therefore, the expression 6x - x^2 - 3 can be written in the form of a(x - h)^2 + k as -(x - 3)^2 - 3.