What is the foci y=x^2+8x+18 ?

The foci y=x^2+8x+18 is (-4, 9/4)

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foci y=x^2+8x+18

foci

y = x^{2} + 8 x + 18

(- 4, \frac{9}{4})

Solution steps

Rewrite

y = x^{2} + 8 x + 18

in the standard form

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

(h, k) = (- 4, 2), p = \frac{1}{4}

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

p

from the center

(- 4, 2)

along the y-axis

(- 4, 2 + p)

= (- 4, 2 + \frac{1}{4})

Refine

(- 4, \frac{9}{4})

5 x^{2} + 6 x - 4

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

y = x^{2} - 2 x - 9

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

x^{2} - 10 x - 20 y = - 185