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

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

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directrix y=-(x-2)^2+4

directrix

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

y = \frac{17}{4}

Solution steps

Rewrite

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

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} - 2 y - 12 x + 25 = 0

y^{2} - 6 x - y + 11 = 0

4 (x + 1)^{2}

x^{2} + 5 x - 24

\frac{1}{24} y^{2}