What is the directrix 2(x-3)^2+6 ?

The directrix 2(x-3)^2+6 is y= 47/8

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directrix 2(x-3)^2+6

directrix

2 (x - 3)^{2} + 6

y = \frac{47}{8}

Solution steps

Rewrite

y = 2 (x - 3)^{2} + 6

in the standard form:

4 \cdot \frac{1}{8} (y - 6) = (x - 3)^{2}

(h, k) = (3, 6), p = \frac{1}{8}

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

(3, 6)

y-coordinate

y = 6 - p

y = 6 - \frac{1}{8}

Refine

y = \frac{47}{8}

y = - 3 x^{2} + 12 x - 8

x^{2} - 6 x - 12 y - 51 = 0

(x + 3)^{2} = 8 (y - 2)

- 8 x^{2}

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