What is the directrix 4-X^2 ?

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directrix 4-X^2

directrix

4 - X^{2}

y = \frac{17}{4}

Solution steps

Rewrite

y = 4 - X^{2}

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}

x^{2} + 4 x - 4 y = 0

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

- x^{2} + 8 x - 7

y = x^{2} - 5 x + 4

y = x^{2} - x - 6