Complete the square and find the vertex from of the quadratic function.
f(x) = -x2+6x-38
Solution:-
Factor the coefficient of x2 out of the first two terms.
f(x) = -x2+6x-38
=-(x2-6x)-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.
=-(x2-6x+9)-38+9
Simplify the square.
=-(x-3)2 – 38 + 9
Simplify the rest of the terms.
f(x) = -(x -3)2 – 29