What is the foci y=-x^2-6x+15 ?

The foci y=-x^2-6x+15 is (-3, 95/4)

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foci y=-x^2-6x+15

foci

y = - x^{2} - 6 x + 15

(- 3, \frac{95}{4})

Solution steps

Rewrite

y = - x^{2} - 6 x + 15

in the standard form

4 (- \frac{1}{4}) (y - 24) = (x - (- 3))^{2}

(h, k) = (- 3, 24), p = - \frac{1}{4}

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

p

from the center

(- 3, 24)

along the y-axis

(- 3, 24 + p)

= (- 3, 24 + (- \frac{1}{4}))

Refine

(- 3, \frac{95}{4})

(x + 3) + (y - 2)^{2} = 0

x = 2 y - y^{2}

- \frac{( x + 3 ) ^{2}}{20} + 1

y = 3 x^{2} - 15 x + 6

- 12 y + 10 = x^{2} - 4 x + 14