What is the directrix x^2+4 ?

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directrix x^2+4

directrix

x^{2} + 4

y = \frac{15}{4}

Solution steps

Rewrite

y = x^{2} + 4

in the standard form:

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

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

y-coordinate

y = 4 - p

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

Refine

y = \frac{15}{4}

x^{2} - 4 x + 5

y = \frac{1}{2} x^{2} + 9 x + 8

x = \frac{1}{4} y^{2}

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

y = 7 x^{2} - 3