What is x^2+x+6k(x)>0 ?

The solution to x^2+x+6k(x)>0 is Parabola with (h,k)=(-1/2 , 1/24),p=-3/2

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x^2+x+6k(x)>0

x^{2} + x + 6 k (x) > 0

(h, k) = (- \frac{1}{2}, \frac{1}{24}), p = - \frac{3}{2}

Solution steps

x^{2} + x + 6 y > 0

Rewrite

x^{2} + x + 6 y > 0

in the standard form

4 (- \frac{3}{2}) (y - \frac{1}{24}) = (x - (- \frac{1}{2}))^{2}

Therefore parabola properties are:

(h, k) = (- \frac{1}{2}, \frac{1}{24}), p = - \frac{3}{2}

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

(x - 2)^{2} = 20 (y - 4)

x^{2} - 10 x - 8 y - 23 = 0

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

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

What is x^2+x+6k(x)>0 ?
The solution to x^2+x+6k(x)>0 is Parabola with (h,k)=(-1/2 , 1/24),p=-3/2