What is the directrix-x^2+4 ?

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directrix-x^2+4

directrix

- x^{2} + 4

y = \frac{17}{4}

Solution steps

Rewrite

y = - x^{2} + 4

in the standard form:

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

(h, k) = (0, 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

(0, 4)

y-coordinate

y = 4 - p

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

Refine

y = \frac{17}{4}

y = + 2 (x + 1)^{2} - 5

x - x^{2}

x^{2} + 2 x - 16 y + 65 = 0

2 x^{2} - 36 x + 324

y = (2 x - 1) (5 x - 6)