y = -x^2 - 16x + 12 = 0
set it equal to 0 to get:
-x^2 - 16x + 12 = 0
you can find the zeroes using the quadratic formula, or you can find the zeroes by using the completing the square method.
we'll use the completing the square method since that will also lead to the vertex form of the equation.
multiply both sides of the equation by -1 to get:
-1 * (x^2 + 16x - 12) = 0
your factored equation will be -1 * the factors of x^2 + 16x - 12.
that's the part that we'll be completing the square method on.
start with:
x^2 + 16x - 12 = 0
take 1/2 the coefficient of the x term and transform to the completing the square form of:
(x + 8)^2 - 12 - 64 = 0
simplify to get:
(x + 8)^2 - 76 = 0
your complete factors are:
(-1) * ((x+8)^2 - 76) = 0
simplify this to get:
-(x+8)^2 + 76 = 0
that's the vertex form of the equation.
now you want to find the roots.
subtract 76 from both sides of the equation to get:
-(x+8)^2 = -76
multiply both sides of the equation by -1 to get:
(x+8)^2 = 76
take the square root of both sides of the equation to get:
x+8 = plus or minus sqrt(76)
subtract 8 from both sides of the equation to get:
x = -8 plus or minus sqrt(76)
those are your roots.
i believe you can simplify this to get;
x = -8 plus or minus 2*sqrt(19).
the graph of your original equation and the vertex form of your original equation are shown below:
-8 - 2*sqrt(19) = -16.72
-8 + 2*sqrt(19) = .72
