What is the directrix y=(2x+1)^2-1 ?

The directrix y=(2x+1)^2-1 is y=-17/16

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directrix y=(2x+1)^2-1

directrix

y = - \frac{17}{16}

Solution steps

Rewrite

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

in the standard form:

4 \cdot \frac{1}{16} (y - (- 1)) = (x - (- \frac{1}{2}))^{2}

(h, k) = (- \frac{1}{2}, - 1), p = \frac{1}{16}

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}, - 1)

y-coordinate

y = - 1 - p

y = - 1 - \frac{1}{16}

Refine

y = - \frac{17}{16}