What is the vertex form of the equation? y = -x^2 + 12x - 4. I have no clue how to do this.

Answer 1

If you have no clue, then clearly you have not studied your material, since it must have been covered.

If a parabola has vertex at (h,k), then the equation is

y = a(x-h)^2+k

You have
y = -x^2+12x-4
= -(x^2-12x) -4

Now recall that (x+n)^2 = x^2+2nx+n^2
That means that you have 2n = -12, or n=-6.

So, add (-6)^2=36 inside the parentheses and you have a perfect square. But, having done that, you have changed the expression, so you have to subtract it as well, so the value is unchanged:

y = -(x^2-12x+36) - 4 + 36
y = -(x-6)^2 + 32

To check you answer, expand things out; it should give you what you started with:

-(x-6)^2+32
= -(x^2-12x+36)+32
= -x^2+12x-36+32
= -x^2+12x-4

Answer 2

Thanks for helping them, but remember, the education system is flawed. Not all teachers do their job (the place I teach at, the other teachers just don't care), not all students understand the material given (some students coming from another school, or had a different learning pace in a previous grade, might not have done the material at all before the new teacher they have expects them to have already learned it), not all students learn the same way (some might not solve word problems as well, some might be visual learners, some might need things read to them, some might need a hands on approach, everyone is different and school only teaches you one way, and if you don't fit the mold, you get left behind in favor of the ones that do), and not all students respect that others may not get it as fast as they do (students who understand it faster get bored easy, and tend to disrupt the learning for the ones who don't get it as quickly).