What is the directrix-2x^2+64x-90 ?

The directrix-2x^2+64x-90 is y= 3377/8

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directrix-2x^2+64x-90

directrix

- 2 x^{2} + 64 x - 90

y = \frac{3377}{8}

Solution steps

Rewrite

y = - 2 x^{2} + 64 x - 90

in the standard form

4 (- \frac{1}{8}) (y - 422) = (x - 16)^{2}

(h, k) = (16, 422), 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

(16, 422)

y-coordinate

y = 422 - p

y = 422 - (- \frac{1}{8})

Refine

y = \frac{3377}{8}

y = \frac{x ^{2} - 4 x - 1}{7}

y^{2} - 28 x = 0

3 y^{2} = - 4 x

(x + 3)^{2} = 4 (y - 1)

y = x^{2} - 4 x - 3