What is the directrix x^2-20x+100 ?

The directrix x^2-20x+100 is y=-1/4

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directrix x^2-20x+100

directrix

x^{2} - 20 x + 100

y = - \frac{1}{4}

Solution steps

Rewrite

y = x^{2} - 20 x + 100

in the standard form

4 \cdot \frac{1}{4} (y - 0) = (x - 10)^{2}

(h, k) = (10, 0), p = \frac{1}{4}

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

(10, 0)

y-coordinate

y = 0 - p

y = 0 - \frac{1}{4}

Refine

y = - \frac{1}{4}

y = 2 x^{2} + 4

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

(x - h)^{2} = 4 p (y - k)

y^{2} + 8 x = 0

y = 2 x^{2} - 4 x + 15