What is the foci 2x^2+8x-24 ?

The foci 2x^2+8x-24 is (-2,-255/8)

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foci 2x^2+8x-24

foci

2 x^{2} + 8 x - 24

(- 2, - \frac{255}{8})

Solution steps

Rewrite

y = 2 x^{2} + 8 x - 24

in the standard form

4 \cdot \frac{1}{8} (y - (- 32)) = (x - (- 2))^{2}

(h, k) = (- 2, - 32), p = \frac{1}{8}

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

p

from the center

(- 2, - 32)

along the y-axis

(- 2, - 32 + p)

= (- 2, - 32 + \frac{1}{8})

Refine

(- 2, - \frac{255}{8})

10 y^{2} = 22 x

y = \frac{- 3 x ^{2} - 2 x + 6}{5}

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

x^{2} = - 10 y

y = 3 x^{2} + 5 x - 4