What is the directrix y=-2x^2+7 ?

The directrix y=-2x^2+7 is y= 57/8

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directrix y=-2x^2+7

directrix

y = - 2 x^{2} + 7

y = \frac{57}{8}

Solution steps

Rewrite

y = - 2 x^{2} + 7

in the standard form:

4 (- \frac{1}{8}) (y - 7) = (x - 0)^{2}

(h, k) = (0, 7), 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, 7)

y-coordinate

y = 7 - p

y = 7 - (- \frac{1}{8})

Refine

y = \frac{57}{8}

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

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

y = 9 x^{2} + 6 x + 1

x^{2} + 4 x + 7

y = 2 x^{2} - 6 x + 4