What is the directrix y=-3x^2+17x-20 ?

The directrix y=-3x^2+17x-20 is y= 25/6

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directrix y=-3x^2+17x-20

directrix

y = - 3 x^{2} + 17 x - 20

y = \frac{25}{6}

Solution steps

Rewrite

y = - 3 x^{2} + 17 x - 20

in the standard form

4 (- \frac{1}{12}) (y - \frac{49}{12}) = (x - \frac{17}{6})^{2}

(h, k) = (\frac{17}{6}, \frac{49}{12}), p = - \frac{1}{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{17}{6}, \frac{49}{12})

y-coordinate

y = \frac{49}{12} - p

y = \frac{49}{12} - (- \frac{1}{12})

Refine

y = \frac{25}{6}

92 x^{2}

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

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

- x^{2} - 4 x - 4

y = x^{2} - 8 x