What is the foci y=4x^2+8x-20 ?

The foci y=4x^2+8x-20 is (-1,-383/16)

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foci y=4x^2+8x-20

foci

y = 4 x^{2} + 8 x - 20

(- 1, - \frac{383}{16})

Solution steps

Rewrite

y = 4 x^{2} + 8 x - 20

in the standard form

4 \cdot \frac{1}{16} (y - (- 24)) = (x - (- 1))^{2}

(h, k) = (- 1, - 24), p = \frac{1}{16}

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

p

from the center

(- 1, - 24)

along the y-axis

(- 1, - 24 + p)

= (- 1, - 24 + \frac{1}{16})

Refine

(- 1, - \frac{383}{16})

x = - \frac{1}{52} (y^{2} + 18 y - 647)

4 x^{2} + 8 x

x^{2} - 13 x + 40

- 2 x^{2} - 8 x - 12

\frac{4 x ^{3} - 7 x ^{2} - 11 x + 5}{4 x + 5}