What is the foci 3x^2-12x+10 ?

The foci 3x^2-12x+10 is (2,-23/12)

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foci 3x^2-12x+10

foci

3 x^{2} - 12 x + 10

(2, - \frac{23}{12})

Solution steps

Rewrite

y = 3 x^{2} - 12 x + 10

in the standard form

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

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

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}{12})

Refine

(2, - \frac{23}{12})

y^{2} = 24 x

y^{2} + 6 y + 9 = x + 8

x^{2} + 2 x + 4

y = 3 - x^{2}

x^{2} = 10 y