What is the directrix y=-x^2+4x ?

The directrix y=-x^2+4x is y= 17/4

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directrix y=-x^2+4x

directrix

y = - x^{2} + 4 x

y = \frac{17}{4}

Solution steps

Rewrite

y = - x^{2} + 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}

y^{2} + 4 x - 14 y = - 53

y = 6 x^{2} + 12 x

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

4 X^{2} + 12 X + 9

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