What is the directrix 1/400 x^2-x+150 ?

The directrix 1/400 x^2-x+150 is y=-50

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directrix 1/400 x^2-x+150

directrix

\frac{1}{400} x^{2} - x + 150

y = - 50

Solution steps

Rewrite

y = \frac{1}{400} x^{2} - x + 150

in the standard form

4 \cdot 100 (y - 50) = (x - 200)^{2}

(h, k) = (200, 50), p = 100

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

(200, 50)

y-coordinate

y = 50 - p

y = 50 - 100

Refine

y = - 50

y = (x - 1) (3 x + 1)

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

2 (x - 3)^{2} + 6

y = - 3 x^{2} + 12 x - 8

x^{2} - 6 x - 12 y - 51 = 0