What is the directrix y=3x^2+4 ?

The directrix y=3x^2+4 is y= 47/12

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directrix y=3x^2+4

directrix

y = 3 x^{2} + 4

y = \frac{47}{12}

Solution steps

Rewrite

y = 3 x^{2} + 4

in the standard form:

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

(h, k) = (0, 4), 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, 4)

y-coordinate

y = 4 - p

y = 4 - \frac{1}{12}

Refine

y = \frac{47}{12}

y = 2 x^{2} - 8 x + 4

3 - t^{2}

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

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

+ 2 x^{2} + 24 x + 76