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

The directrix 3x^2-30x+77 is y= 23/12

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directrix 3x^2-30x+77

directrix

3 x^{2} - 30 x + 77

y = \frac{23}{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 directrix is a line parallel to the x-axis, a distance

- p

from the center

(5, 2)

y-coordinate

y = 2 - p

y = 2 - \frac{1}{12}

Refine

y = \frac{23}{12}

y = 2 x^{2} + 28 x + 105

(x - 1)^{2} = - 2 y - 11

(x - 2)^{2} = 8 (y + 1)

y^{2} = 24 x

y = - \frac{( x + 3 ) ^{2}}{20} + 1