What is the directrix x^2+3 ?

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directrix x^2+3

directrix

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^{2} = - 6 x

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

4 x^{2}

y = 4 x^{2} - 4 x^{1}

y = 3 x^{2} - x + 5