What is the directrix y=(-3x^2-2x+6)/5 ?

The directrix y=(-3x^2-2x+6)/5 is y= 101/60

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directrix y=(-3x^2-2x+6)/5

directrix

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

y = \frac{101}{60}

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 directrix is a line parallel to the x-axis, a distance

- p

from the center

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

y-coordinate

y = \frac{19}{15} - p

y = \frac{19}{15} - (- \frac{5}{12})

Refine

y = \frac{101}{60}

X^{2}

x^{2} + 2 x + 3

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

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

x^{2} + 3

What is the directrix y=(-3x^2-2x+6)/5 ?
The directrix y=(-3x^2-2x+6)/5 is y= 101/60