What is the directrix-2x^2+11 ?

The directrix-2x^2+11 is y= 89/8

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directrix-2x^2+11

directrix

- 2 x^{2} + 11

y = \frac{89}{8}

Solution steps

Rewrite

y = - 2 x^{2} + 11

in the standard form:

4 (- \frac{1}{8}) (y - 11) = (x - 0)^{2}

(h, k) = (0, 11), 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

(0, 11)

y-coordinate

y = 11 - p

y = 11 - (- \frac{1}{8})

Refine

y = \frac{89}{8}

y = (x - 4) (x - 7)

y = - 2 x^{2} + 6

y = - 2 x^{2} + 7

y = (7 x - 3)^{2}

+ 6 x^{2} - 54 x + 120