What is the directrix+2(x+1)^2-3 ?

The directrix+2(x+1)^2-3 is y=-25/8

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directrix+2(x+1)^2-3

directrix

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

y = - \frac{25}{8}

Solution steps

Rewrite

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

in the standard form:

4 \cdot \frac{1}{8} (y - (- 3)) = (x - (- 1))^{2}

(h, k) = (- 1, - 3), p = \frac{1}{8}

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

(- 1, - 3)

y-coordinate

y = - 3 - p

y = - 3 - \frac{1}{8}

Refine

y = - \frac{25}{8}

x^{2} - 6 y = 0

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

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

y = x^{2} + 10 x - 96

4 (x + 2)^{2} + 5