Sister Queen Anne and Pastor here is the first problem
f(x)=-3x^2+6x-1
Start by factoring -3 from the first two terms, don’t factor it out from the third
f(x)=-3(x^2-2x)-1
Next complete the square for the second term, and add and subtract it within the parenthesis. By adding and subtracting the completed square term you are adding zero which doesn’t change anything.
(-2/2)^2=1
f(x)=-3(x^2-2x+1-1)-1
The next step, you are going to move the – 1 out of the parentheses but it has a factor of -3 attached to it so it ends up being 3
f(x)= -3(x^2-2x+1)-1+3
The term in the parentheses is a perfect square, -1 and 3 are like terms, so you put the term in parentheses in squared term and add the negative 1 and positive 3
f(x)= -3(x-1)^2+2
