Put the equation in vertex form: y^2=12x-2y+250 using the formula y=a(x-h)^2+k

Thanks in advance :]

Oops, its y^2 - 12x - 2y + 25 = 0

We would not state your parabola in the form

y = a(x-h)^2 + k, because your parabola has a horizontal axis of symmetry (lays sideways)

anyway ....

12x = y^2 + 2y - 250
12x = y^2 + 2y + 1 - 1 - 250
12x = (y+1)^2 - 251

x = (1/12)(y+1)^2 - 251/12

notice the similarity between the parabola equations, the x and y variables have been interchanged. So to state the vertex we also have to
interchange the variables.

the vertex is (-251/12, -1)

check my arithmetic

12x = y^2 - 2y + 25

12x = y^2 - 2y + 1 - 1 + 25
12x = (y-1)^2 + 24
x = (1/12)(y-1)^2 + 2

vertex is (2, 1)

To put the equation y^2 = 12x - 2y + 250 in vertex form, which is y = a(x - h)^2 + k, we need to complete the square.

First, let's rearrange the equation by moving the terms with y to one side:

y^2 + 2y = 12x + 250

To complete the square for the y terms, we need to add and subtract the square of half of the coefficient of y:

y^2 + 2y + (2/2)^2 = 12x + 250 + (2/2)^2
(y + 1)^2 = 12x + 250 + 1

Simplifying further, we have:

(y + 1)^2 = 12x + 251

Now, we can rewrite the equation in vertex form:

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

Comparing this with our equation (y + 1)^2 = 12x + 251, we see that a = 1, h = 0, and k = 251.

Therefore, the equation y^2 = 12x - 2y + 250 in vertex form is y = (x - 0)^2 + 251.