What is 2x^2=2(x-1)+k(x) ?

The solution to 2x^2=2(x-1)+k(x) is Parabola with (h,k)=(1/2 , 3/2),p= 1/8

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

2 x^{2} = 2 (x - 1) + k (x)

(h, k) = (\frac{1}{2}, \frac{3}{2}), p = \frac{1}{8}

Solution steps

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

Rewrite

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

in the standard form

4 \cdot \frac{1}{8} (y - \frac{3}{2}) = (x - \frac{1}{2})^{2}

Therefore parabola properties are:

(h, k) = (\frac{1}{2}, \frac{3}{2}), p = \frac{1}{8}

y^{2} - 8 y = 6 x - 16

y^{2} - 2 y - 4 x + 9 = 0

(y - 3)^{2} = - 8 x

2 y^{2} - 8 x = 0

y^{2} + 3 = x

What is 2x^2=2(x-1)+k(x) ?
The solution to 2x^2=2(x-1)+k(x) is Parabola with (h,k)=(1/2 , 3/2),p= 1/8