Algebra 2 ! 17. )what is the vertex form of the equation? y=-x^2+12x-4
show me how to do it with steps and explain! i'm so confused. so much!

Well to start, vertex form is y=a(x-h)^2+k, where (h,k) is the vertex. a in this problem would be -1 because a is the constant before x^2. So, the sign on a tells you whether the quadratic opens up or opens down.

Your quadratic opens down. So to make this in vertex form you just plug it in.

y=(-1)(x-h)^2 +k

Now we have to figure out what h and k are.

h= -b/2a
h= -12/2(-1)
h= 6

So now your equation is y=(-1)(x-6)^2 +k

Now lets figure out what k is.

k= 4ac-b^2/4a
k=4(-1)(-4)-12^2
k=16+144
k=160/4(-1)
k=160/-4
k=-40

So your final equation is -1(x-6)^2-40

11^2 + 9^2 = c^2
121 + 81 = c^2
202= c^2
Square root(202)= square root(c)
14.213= c
Hypotenuse = 14.213