Question

Y=-x^2+12x-4Complete the square for - x^2+12x-4Use ax^2+bx+cA=-1, b=12, c=-4

Answer 1

The given equation is

$y=-x^2+12x-4$

To complete the square take -1 as a common factor from the right side

$-x^2+12x-4=-1(x^2-12x+4)$

Divide the term of x by 2 to find the product of the first and second terms in the bracket

$\frac{-12x}{2}=-6x$

The bracket will be (x - 6)

Square it

$(x-6)^2=x^2-12x+36$

Then add and subtract (36 - 4)

$-\lbrack(x^2-12x+4+32)-32\rbrack=-(x^2-12x+36)+32$

Make the trinomial a square binomial

$-(x^2-12x+36)-32=-(x-6)^2+32$

The completing square is

$-x^2+12x-4=-(x-6)^2+32$