What is the foci-2x^2-16x-25 ?

The foci-2x^2-16x-25 is (-4, 55/8)

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foci-2x^2-16x-25

foci

- 2 x^{2} - 16 x - 25

(- 4, \frac{55}{8})

Solution steps

Rewrite

y = - 2 x^{2} - 16 x - 25

in the standard form

4 (- \frac{1}{8}) (y - 7) = (x - (- 4))^{2}

(h, k) = (- 4, 7), p = - \frac{1}{8}

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

p

from the center

(- 4, 7)

along the y-axis

(- 4, 7 + p)

= (- 4, 7 + (- \frac{1}{8}))

Refine

(- 4, \frac{55}{8})

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

- x^{2} + 10 x - 23

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

x^{2} - 5 x + 6

(x + 2)^{2} = - 6 (y - 1)