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

The directrix 1/4 x^2+x-8 is y=-10

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directrix 1/4 x^2+x-8

directrix

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

y = - 10

Solution steps

Rewrite

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

in the standard form

4 \cdot 1 \cdot (y - (- 9)) = (x - (- 2))^{2}

(h, k) = (- 2, - 9), 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

(- 2, - 9)

y-coordinate

y = - 9 - p

y = - 9 - 1

Refine

y = - 10

x^{2} - 8 x - 240

- 2 x^{2} - 4 x + 34

2 x^{2} - 5 x + 5

y = \frac{x ^{2} 5 x 8}{x 3}

(x + 5)^{2} = - 20 (y - 2)