What is the foci 3x^2-30x+77 ?

The foci 3x^2-30x+77 is (5, 25/12)

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foci 3x^2-30x+77

foci

3 x^{2} - 30 x + 77

(5, \frac{25}{12})

Solution steps

Rewrite

y = 3 x^{2} - 30 x + 77

in the standard form

4 \cdot \frac{1}{12} (y - 2) = (x - 5)^{2}

(h, k) = (5, 2), p = \frac{1}{12}

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

p

from the center

(5, 2)

along the y-axis

(5, 2 + p)

= (5, 2 + \frac{1}{12})

Refine

(5, \frac{25}{12})

2 x^{2} - 36 x + 324

y = a x^{2}

y = (2 X + 5) (3 X - 7)

y = \frac{1}{2} x^{2}

y^{2} = 5 y + 7 x + 3