What is the directrix 4-x-x^2 ?

The directrix 4-x-x^2 is y= 9/2

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directrix 4-x-x^2

directrix

4 - x - x^{2}

y = \frac{9}{2}

Solution steps

Rewrite

y = 4 - x - x^{2}

in the standard form

4 (- \frac{1}{4}) (y - \frac{17}{4}) = (x - (- \frac{1}{2}))^{2}

(h, k) = (- \frac{1}{2}, \frac{17}{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

(- \frac{1}{2}, \frac{17}{4})

y-coordinate

y = \frac{17}{4} - p

y = \frac{17}{4} - (- \frac{1}{4})

Refine

y = \frac{9}{2}

y = - 7 (x - 8)^{2} + 6

y = x^{2} - 9 x + 20

x^{2} - 6 x + 5 y = 34

y = (x - 4)^{2} - 9

y = \frac{1}{3} x^{2} + 6 x + 10