What is the directrix+x^2+12 ?

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

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directrix+x^2+12

directrix

+ x^{2} + 12

y = \frac{47}{4}

Solution steps

Rewrite

y = x^{2} + 12

in the standard form:

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

(h, k) = (0, 12), p = \frac{1}{4}

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, 12)

y-coordinate

y = 12 - p

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

Refine

y = \frac{47}{4}

y = 5 x^{2} + 210 x - 34775

y^{2} - 6 y - 4 x + 5 = 0

(x + 2)^{2} = - 6 (y - 1)

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

- \frac{1}{4} x^{2} + 8 x - 4