What is 2x^2+4x+5k(x)=0 ?

The solution to 2x^2+4x+5k(x)=0 is Parabola with (h,k)=(-1, 2/5),p=-5/8

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2x^2+4x+5k(x)=0

2 x^{2} + 4 x + 5 k (x) = 0

(h, k) = (- 1, \frac{2}{5}), p = - \frac{5}{8}

Solution steps

2 x^{2} + 4 x + 5 y = 0

Rewrite

2 x^{2} + 4 x + 5 y = 0

in the standard form

4 (- \frac{5}{8}) (y - \frac{2}{5}) = (x - (- 1))^{2}

Therefore parabola properties are:

(h, k) = (- 1, \frac{2}{5}), p = - \frac{5}{8}

x^{2} + 2 x + 4 y - 19 = 0

x + y^{2} = 6

y \leq x^{2} - 3

x + y^{2} = 2

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

What is 2x^2+4x+5k(x)=0 ?
The solution to 2x^2+4x+5k(x)=0 is Parabola with (h,k)=(-1, 2/5),p=-5/8