What is 2x^2-2x+k(x)-3=0 ?

The solution to 2x^2-2x+k(x)-3=0 is Parabola with (h,k)=(1/2 , 7/2),p=-1/8

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2x^2-2x+k(x)-3=0

2 x^{2} - 2 x + k (x) - 3 = 0

(h, k) = (\frac{1}{2}, \frac{7}{2}), p = - \frac{1}{8}

Solution steps

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

Rewrite

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

in the standard form

4 (- \frac{1}{8}) (y - \frac{7}{2}) = (x - \frac{1}{2})^{2}

Therefore parabola properties are:

(h, k) = (\frac{1}{2}, \frac{7}{2}), p = - \frac{1}{8}

(y + 3)^{2} = 16 (x - 9)

y^{2} + 8 x + 4 y + 20 = 0

x^{2} - 6 x - 6 y - 21 = 0

(y - 3)^{2} = - 6 (x + 4)

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

What is 2x^2-2x+k(x)-3=0 ?
The solution to 2x^2-2x+k(x)-3=0 is Parabola with (h,k)=(1/2 , 7/2),p=-1/8