What is the directrix 1/4 x^2 ?

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directrix 1/4 x^2

directrix

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

y = - 1

Solution steps

Rewrite

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

in the standard form:

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

(h, k) = (0, 0), p = 1

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, 0)

y-coordinate

y = 0 - p

y = 0 - 1

Refine

y = - 1

3 y^{2} - 30 y + 77

(x - 3)^{2} + 1

x^{2} = - 6 y

y = - 12 x^{2} + 4 x

x = \frac{1}{12} y^{2}