What is the directrix x^2+2x+3 ?

The directrix x^2+2x+3 is y= 7/4

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directrix x^2+2x+3

directrix

x^{2} + 2 x + 3

y = \frac{7}{4}

Solution steps

Rewrite

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

in the standard form

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

(h, k) = (- 1, 2), 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, 2)

y-coordinate

y = 2 - p

y = 2 - \frac{1}{4}

Refine

y = \frac{7}{4}

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

y = 2 x^{2} + 5 x - 7

x^{2} + 3

y^{2} = - 6 x

(x - 1)^{2} = 16 (y - 2)