What is the directrix 4P^2 ?

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directrix 4P^2

directrix

4 P^{2}

y = - \frac{1}{16}

Solution steps

Rewrite

y = 4 P^{2}

in the standard form:

4 \cdot \frac{1}{16} (y - 0) = (P - 0)^{2}

(h, k) = (0, 0), p = \frac{1}{16}

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 - \frac{1}{16}

Refine

y = - \frac{1}{16}

x^{2} + 3 x - 16

2 x - x^{2}

y = (x - 12)^{2} - 156

y = x^{2} + 6 x + 11

- x (x - 3)