What is the foci y=-x^2-4x-2 ?

The foci y=-x^2-4x-2 is (-2, 7/4)

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foci y=-x^2-4x-2

foci

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

(- 2, \frac{7}{4})

Solution steps

Rewrite

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

in the standard form

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

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

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

p

from the center

(- 2, 2)

along the y-axis

(- 2, 2 + p)

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

Refine

(- 2, \frac{7}{4})

(y - 2)^{2} - 3

x^{2} + 6 x + 16

x = - 2 (y - 2)^{2} + 7

(2 x - 1) (5 x - 6)

20 t - t^{2}