What is y^{(2)}+4y+8x-12=0 ?

The solution to y^{(2)}+4y+8x-12=0 is Parabola with (h,k)=(2,-2),p=-2

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y^{(2)}+4y+8x-12=0

y^{(2)} + 4 y + 8 x - 12 = 0

(h, k) = (2, - 2), p = - 2

Solution steps

y^{2} + 4 y + 8 x - 12 = 0

Rewrite

y^{2} + 4 y + 8 x - 12 = 0

in the standard form

4 (- 2) (x - 2) = (y - (- 2))^{2}

Therefore parabola properties are:

(h, k) = (2, - 2), p = - 2

x = \frac{1}{4} (y + 4)^{2} + 2

(y - 6)^{2} = - \frac{3}{2} (x + 2)

3 f (x) = 2 x^{2} - 3 x

(x + 0)^{2} = - 8 (y + 1)

y^{2} - 2 y - 3 x - 8 = 0

What is y^{(2)}+4y+8x-12=0 ?
The solution to y^{(2)}+4y+8x-12=0 is Parabola with (h,k)=(2,-2),p=-2