What is the directrix x^2+4x+7 ?

The directrix x^2+4x+7 is y= 11/4

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directrix x^2+4x+7

directrix

x^{2} + 4 x + 7

y = \frac{11}{4}

Solution steps

Rewrite

y = x^{2} + 4 x + 7

in the standard form

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

(h, k) = (- 2, 3), 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, 3)

y-coordinate

y = 3 - p

y = 3 - \frac{1}{4}

Refine

y = \frac{11}{4}

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

\frac{( x - 5 ) ( x - 10 )}{50}

2 x^{2} - 12 x + 14 - 14 y = 0

(4 - x)^{2}

y = 7 x^{2}