Question

I need help converting standard form to vertex form with quadratic equations. The equation is: y = -x^2 + 12x -4I think I am supposed to complete the square, but I am unsure how to do this. I am also unsure about what to do with the negative sign. I would love clear, step by step instructions on the process so I can know how to do it in the future.

Answer 1

Okay, here we have this:

Considering the provided equation in standard form, we are going to convert it to vertex form step by step, so we obtain the following:

y = -x²+ 12x -4

Considering that the model of an equation in standard form is y=ax²+bx+c. First we are going to axtract "a" from the first two terms:

y=-1(x²-12x)-4

Now, we are going to complete the square for the expressions with x, so we have:

y=-1(x²-12x+36-36)-4

y=-1((x - 6)²-36) -4

And, finally we are going to simplify:

y=-1(x - 6)²+36-4

y=-(x - 6)²+32

We obtain that the equation in vertex form is y=-(x - 6)²+32.