What is the foci y=+3x^2+24x-51 ?

The foci y=+3x^2+24x-51 is (-4,-1187/12)

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foci y=+3x^2+24x-51

foci

y = + 3 x^{2} + 24 x - 51

(- 4, - \frac{1187}{12})

Solution steps

Rewrite

y = 3 x^{2} + 24 x - 51

in the standard form

4 \cdot \frac{1}{12} (y - (- 99)) = (x - (- 4))^{2}

(h, k) = (- 4, - 99), p = \frac{1}{12}

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

p

from the center

(- 4, - 99)

along the y-axis

(- 4, - 99 + p)

= (- 4, - 99 + \frac{1}{12})

Refine

(- 4, - \frac{1187}{12})

x = (2 y - 1)^{2}

y = x^{2} - 10 x - 24

y = 92 x^{2}

y^{2} = 40 x

y = - 7 (x - 8)^{2} + 6