What is the foci-12x^2-29x+230 ?

The foci-12x^2-29x+230 is (-29/24 , 495/2)

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foci-12x^2-29x+230

foci

- 12 x^{2} - 29 x + 230

(- \frac{29}{24}, \frac{495}{2})

Solution steps

Rewrite

y = - 12 x^{2} - 29 x + 230

in the standard form

4 (- \frac{1}{48}) (y - \frac{11881}{48}) = (x - (- \frac{29}{24}))^{2}

(h, k) = (- \frac{29}{24}, \frac{11881}{48}), p = - \frac{1}{48}

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

p

from the center

(- \frac{29}{24}, \frac{11881}{48})

along the y-axis

(- \frac{29}{24}, \frac{11881}{48} + p)

= (- \frac{29}{24}, \frac{11881}{48} + (- \frac{1}{48}))

Refine

(- \frac{29}{24}, \frac{495}{2})

y = x^{2} - 3 x

y = - 45 x^{2} - 27 x + 2

(x - 1)^{2} + 5

y = x^{2} + 4

y = x^{2} - 4