Complete the square.... y = x^2 - 12x - 4?

Question

..... Use completing the square to write this equation in y = (x- h)^2 + k


The equation is: y = (x - __)^2 - __

The Vertex is ___

The Focus is ____

The Directrix is y = ____

Thank you so much for the help!!!

Answer 1

y = x² - 12x ...... -4

The number that completes the square is 1/2 of the number in front of x, squared. We need to add that, but we also need to subtract it, in order to make the equation still balance.

y = x² - 12x + 36 -4-36

y = (x-6)² - 40

The rest is all you.

Answer 2

Put it as (x-c)^2 = x^2 -2cx +c^2 so 2c=12 c= 6 and c^2 =36 so your equation is

y=(x-6)^2 -40

You can follw on

Answer 3

y = (x - 6)^2 - 40
because (a-b)^2 = a^2 - 2*a*b +b^2
2*a*b has to be 12*x (x=a, 12/2=6=b)
and b^2=36... should be -4. 36 - 40 = -4