What is the directrix y=x^2-4x3 ?

The directrix y=x^2-4x3 is y=-145/4

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directrix y=x^2-4x3

directrix

y = x^{2} - 4 x 3

y = - \frac{145}{4}

Solution steps

Rewrite

y = x^{2} - 4 x \cdot 3

in the standard form

4 \cdot \frac{1}{4} (y - (- 36)) = (x - 6)^{2}

(h, k) = (6, - 36), 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

(6, - 36)

y-coordinate

y = - 36 - p

y = - 36 - \frac{1}{4}

Refine

y = - \frac{145}{4}

y^{2} + 16 x = 0

y^{2} + 28 x = 0

y = 4 x^{2} - 24 x + 31

y = - x^{2} + 4 x

y^{2} + 4 x - 14 y = - 53