What is the directrix y=-2x^2+8x ?

The directrix y=-2x^2+8x is y= 65/8

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directrix y=-2x^2+8x

directrix

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

y = \frac{65}{8}

Solution steps

Rewrite

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

in the standard form

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

(h, k) = (2, 8), 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

(2, 8)

y-coordinate

y = 8 - p

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

Refine

y = \frac{65}{8}

y = - 4 x^{2} - 4

(x - 4)^{2} = - 8 (y + 3)

y^{2} + 33 = - 8 x - 23

x^{2} + 7 x + 12

- x^{2} + 1