What is the directrix-1/4 x^2+8x-4 ?

The directrix-1/4 x^2+8x-4 is y=61

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directrix-1/4 x^2+8x-4

directrix

- \frac{1}{4} x^{2} + 8 x - 4

y = 61

Solution steps

Rewrite

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

in the standard form

4 (- 1) (y - 60) = (x - 16)^{2}

(h, k) = (16, 60), p = - 1

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, 60)

y-coordinate

y = 60 - p

y = 60 - (- 1)

Refine

y = 61

y^{2} = 10 x

x^{2} + 1

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

y = 9 x^{2}

x = \frac{1}{8} y^{2}