What is the directrix y=(x-12)^2-156 ?

The directrix y=(x-12)^2-156 is y=-625/4

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directrix y=(x-12)^2-156

directrix

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

y = - \frac{625}{4}

Solution steps

Rewrite

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

in the standard form:

4 \cdot \frac{1}{4} (y - (- 156)) = (x - 12)^{2}

(h, k) = (12, - 156), 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

(12, - 156)

y-coordinate

y = - 156 - p

y = - 156 - \frac{1}{4}

Refine

y = - \frac{625}{4}

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

- x (x - 3)

+ \frac{17}{4} (x + 2)^{2}

y = (- x)^{2}

(x - 3)^{2} = 4 (y + 5)