What is the foci-3x^2+3x-13 ?

The foci-3x^2+3x-13 is (1/2 ,-37/3)

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foci-3x^2+3x-13

foci

- 3 x^{2} + 3 x - 13

(\frac{1}{2}, - \frac{37}{3})

Solution steps

Rewrite

y = - 3 x^{2} + 3 x - 13

in the standard form

4 (- \frac{1}{12}) (y - (- \frac{49}{4})) = (x - \frac{1}{2})^{2}

(h, k) = (\frac{1}{2}, - \frac{49}{4}), p = - \frac{1}{12}

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

p

from the center

(\frac{1}{2}, - \frac{49}{4})

along the y-axis

(\frac{1}{2}, - \frac{49}{4} + p)

= (\frac{1}{2}, - \frac{49}{4} + (- \frac{1}{12}))

Refine

(\frac{1}{2}, - \frac{37}{3})

y = - 2 x^{2} + 5 x - 6

x^{2} + 8 x - 5

12 x^{2} + 12 x + 1

- x^{2} + 8 x - 13

x^{2} = - 9 y