What is the directrix x^2+1 ?

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directrix x^2+1

directrix

x^{2} + 1

y = \frac{3}{4}

Solution steps

Rewrite

y = x^{2} + 1

in the standard form:

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

(h, k) = (0, 1), 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, 1)

y-coordinate

y = 1 - p

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

Refine

y = \frac{3}{4}

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

y = 9 x^{2}

x = \frac{1}{8} y^{2}

y = 2 x^{2} + 6 x + 10

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