What is the directrix 3x^2-5 ?

The directrix 3x^2-5 is y=-61/12

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directrix 3x^2-5

directrix

3 x^{2} - 5

y = - \frac{61}{12}

Solution steps

Rewrite

y = 3 x^{2} - 5

in the standard form:

4 \cdot \frac{1}{12} (y - (- 5)) = (x - 0)^{2}

(h, k) = (0, - 5), 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

(0, - 5)

y-coordinate

y = - 5 - p

y = - 5 - \frac{1}{12}

Refine

y = - \frac{61}{12}

\frac{4 x ^{3} - 7 x ^{2} - 11 x + 5}{4 x + 5}

(\frac{1}{2} - x) (- \frac{1}{2} - x)

y = - 8 x^{2}

3 x^{2} - x

x^{2} + 14 x + 46