What is 2x^2-5x+2k(x)-2=0 ?

The solution to 2x^2-5x+2k(x)-2=0 is Parabola with (h,k)=(5/4 , 41/16),p=-1/4

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2x^2-5x+2k(x)-2=0

2 x^{2} - 5 x + 2 k (x) - 2 = 0

(h, k) = (\frac{5}{4}, \frac{41}{16}), p = - \frac{1}{4}

Solution steps

2 x^{2} - 5 x + 2 y - 2 = 0

Rewrite

2 x^{2} - 5 x + 2 y - 2 = 0

in the standard form

4 (- \frac{1}{4}) (y - \frac{41}{16}) = (x - \frac{5}{4})^{2}

Therefore parabola properties are:

(h, k) = (\frac{5}{4}, \frac{41}{16}), p = - \frac{1}{4}

x - y = 5 (x + 1)^{2} - 3

y^{2} + 2 y + 1 = - 2 x + 4

x - 8 y^{2} = 0

x = \frac{y ^{2}}{7}

y^{2} - 5 y - 8 = 5 x

What is 2x^2-5x+2k(x)-2=0 ?
The solution to 2x^2-5x+2k(x)-2=0 is Parabola with (h,k)=(5/4 , 41/16),p=-1/4