What is the directrix y=(x-4)^2-9 ?

The directrix y=(x-4)^2-9 is y=-37/4

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directrix y=(x-4)^2-9

directrix

y = (x - 4)^{2} - 9

y = - \frac{37}{4}

Solution steps

Rewrite

y = (x - 4)^{2} - 9

in the standard form:

4 \cdot \frac{1}{4} (y - (- 9)) = (x - 4)^{2}

(h, k) = (4, - 9), 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

(4, - 9)

y-coordinate

y = - 9 - p

y = - 9 - \frac{1}{4}

Refine

y = - \frac{37}{4}

y = \frac{1}{3} x^{2} + 6 x + 10

F = \frac{m v ^{2}}{r}

- x^{2} + 6 x + 1

y = 3 x^{2} + 1 - (x + 4)

x^{2} = 8 (y + 4)