What is the foci (-3x^2-2x+6)/5 ?

The foci (-3x^2-2x+6)/5 is (-1/3 , 17/20)

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foci (-3x^2-2x+6)/5

foci

\frac{- 3 x ^{2} - 2 x + 6}{5}

(- \frac{1}{3}, \frac{17}{20})

Solution steps

Rewrite

y = \frac{- 3 x ^{2} - 2 x + 6}{5}

in the standard form

4 (- \frac{5}{12}) (y - \frac{19}{15}) = (x - (- \frac{1}{3}))^{2}

(h, k) = (- \frac{1}{3}, \frac{19}{15}), p = - \frac{5}{12}

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

p

from the center

(- \frac{1}{3}, \frac{19}{15})

along the y-axis

(- \frac{1}{3}, \frac{19}{15} + p)

= (- \frac{1}{3}, \frac{19}{15} + (- \frac{5}{12}))

Refine

(- \frac{1}{3}, \frac{17}{20})

(y - 3)^{2} = - 12 x

(x - 2) = 3 (y - 5)^{2}

(x - 3)^{2} = 8 (y - 5)

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

3 - x^{2}