What is the foci-2x^2-12x-23 ?

The foci-2x^2-12x-23 is (-3,-41/8)

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foci-2x^2-12x-23

foci

- 2 x^{2} - 12 x - 23

(- 3, - \frac{41}{8})

Solution steps

Rewrite

y = - 2 x^{2} - 12 x - 23

in the standard form

4 (- \frac{1}{8}) (y - (- 5)) = (x - (- 3))^{2}

(h, k) = (- 3, - 5), p = - \frac{1}{8}

Parabola is symmetric around the y-axis and so the focus lies a distance

p

from the center

(- 3, - 5)

along the y-axis

(- 3, - 5 + p)

= (- 3, - 5 + (- \frac{1}{8}))

Refine

(- 3, - \frac{41}{8})

2 y = 3 x^{2} + x

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

y^{2} - 12 x - 2 y - 25 = 0

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

x = - \frac{1}{52} (y^{2} + 18 y - 647)