What is the directrix+y=x^2+2x-3 ?

The directrix+y=x^2+2x-3 is y=-17/4

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directrix+y=x^2+2x-3

directrix

+ y = x^{2} + 2 x - 3

y = - \frac{17}{4}

Solution steps

Rewrite

y = x^{2} + 2 x - 3

in the standard form

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

(h, k) = (- 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

(- 1, - 4)

y-coordinate

y = - 4 - p

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

Refine

y = - \frac{17}{4}

8 - 3 x - 2 x^{2}

(x + 2)^{2} = - 12 (y - 5)

y^{2} + 14 y + 4 x + 45 = 0

2 x^{2} + x - 3

y = x^{2} - 8 x + 7