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

The directrix-2-x+x^2 is y=-5/2

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directrix-2-x+x^2

directrix

- 2 - x + x^{2}

y = - \frac{5}{2}

Solution steps

Rewrite

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

in the standard form

4 \cdot \frac{1}{4} (y - (- \frac{9}{4})) = (x - \frac{1}{2})^{2}

(h, k) = (\frac{1}{2}, - \frac{9}{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{9}{4})

y-coordinate

y = - \frac{9}{4} - p

y = - \frac{9}{4} - \frac{1}{4}

Refine

y = - \frac{5}{2}

(x - 1)^{2} - 2

y^{2} - 10 y + 4 x + 25 = 0

(x + 4)^{2} = - 6 (y - 3)

(x - 3)^{2} = \frac{1}{2} (y + 1)

y = (x - 3)^{2} - 2