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

The directrix y=x^2+3 is y= 11/4

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directrix y=x^2+3

directrix

y = x^{2} + 3

y = \frac{11}{4}

Solution steps

Rewrite

y = x^{2} + 3

in the standard form:

4 \cdot \frac{1}{4} (y - 3) = (x - 0)^{2}

(h, k) = (0, 3), 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, 3)

y-coordinate

y = 3 - p

y = 3 - \frac{1}{4}

Refine

y = \frac{11}{4}

y = x^{2} + 1

y = x^{2} + x - 1

4 x^{2} - 8 x - 3 y - 2 = 0

0 = (y - 1)^{2} - 16 (x + 4)

(x + 6)^{2} = 12 (y + 1)