What is the directrix+x^2+4x+6 ?

The directrix+x^2+4x+6 is y= 7/4

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directrix+x^2+4x+6

directrix

+ x^{2} + 4 x + 6

y = \frac{7}{4}

Solution steps

Rewrite

y = x^{2} + 4 x + 6

in the standard form

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

(h, k) = (- 2, 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

(- 2, 2)

y-coordinate

y = 2 - p

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

Refine

y = \frac{7}{4}

\frac{( x - 3 ) ^{2}}{8} + 5

x = 3 y^{2} - 6 y + 5

(y + 1)^{2} = 12 x

(y - 2)^{2} = 40 (x - 2)

(x - 3)^{2} - 1