What is the directrix y=x+x^2 ?

The directrix y=x+x^2 is y=-1/2

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directrix y=x+x^2

directrix

y = x + x^{2}

y = - \frac{1}{2}

Solution steps

Rewrite

y = x + x^{2}

in the standard form

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

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

y-coordinate

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

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

Refine

y = - \frac{1}{2}

4 x - 11 y^{2} = 0

+ (y - 2) = 3 (x - 5)^{2}

x^{2} = 16 (y - 9)

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

x = (y + 3)^{2}