What is the directrix y=-4(x+10)^2+6 ?

The directrix y=-4(x+10)^2+6 is y= 97/16

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directrix y=-4(x+10)^2+6

directrix

y = - 4 (x + 10)^{2} + 6

y = \frac{97}{16}

Solution steps

Rewrite

y = - 4 (x + 10)^{2} + 6

in the standard form:

4 (- \frac{1}{16}) (y - 6) = (x - (- 10))^{2}

(h, k) = (- 10, 6), 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

(- 10, 6)

y-coordinate

y = 6 - p

y = 6 - (- \frac{1}{16})

Refine

y = \frac{97}{16}

y^{2} - 12 y - 4 x + 28 = 0

\frac{6 x}{7} \cdot \frac{4 x}{3}

9 y^{2} - 6 y - 9 - x = 0

2 X^{2}

x^{2} + 3 x - 4