What is the directrix x^2-6 ?

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directrix x^2-6

directrix

x^{2} - 6

y = - \frac{25}{4}

Solution steps

Rewrite

y = x^{2} - 6

in the standard form:

4 \cdot \frac{1}{4} (y - (- 6)) = (x - 0)^{2}

(h, k) = (0, - 6), 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, - 6)

y-coordinate

y = - 6 - p

y = - 6 - \frac{1}{4}

Refine

y = - \frac{25}{4}

4 x^{2} + 3 x - 1

x^{2} + a

y = - \frac{1}{4} (x^{2} - 14 x + 13)

x^{2} + 5

y^{2} = - 32 x