What is the directrix x(4-x) ?

The directrix x(4-x) is y= 17/4

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directrix x(4-x)

directrix

y = \frac{17}{4}

Solution steps

Rewrite

y = x (4 - x)

in the standard form

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

(h, k) = (2, 4), 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

(2, 4)

y-coordinate

y = 4 - p

y = 4 - (- \frac{1}{4})

Refine

y = \frac{17}{4}