Complete the square and find the vertex from of the quadratic function.

f(x) = -x^{2}+6x-38

**Solution:-**

Factor the coefficient of x^{2} out of the first two terms.

f(x) = -x^{2}+6x-38

=-(x^{2}-6x)-38

Add 9 to inside and outside the parentheses to complete the square. 9 is added to the outside of the parentheses instead if subtracted the coefficient is -1.

=-(x^{2}-6x+9)-38+9

Simplify the square.

=-(x-3)^{2} – 38 + 9

Simplify the rest of the terms.

f(x) = -(x -3)^{2} – 29