What is the foci x^2-24x-12 ?

The foci x^2-24x-12 is (12,-623/4)

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foci x^2-24x-12

foci

x^{2} - 24 x - 12

(12, - \frac{623}{4})

Solution steps

Rewrite

y = x^{2} - 24 x - 12

in the standard form

4 \cdot \frac{1}{4} (y - (- 156)) = (x - 12)^{2}

(h, k) = (12, - 156), p = \frac{1}{4}

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

p

from the center

(12, - 156)

along the y-axis

(12, - 156 + p)

= (12, - 156 + \frac{1}{4})

Refine

(12, - \frac{623}{4})

s^{2} + 4 s + 20

y = x^{2} + 5 x + 6

x^{2} + 3 x - 4

(x - 3)^{2} = 8 (y - 2)

(x + 3)^{2} = 24 (y - 1)