What is the directrix x^2+8x+3 ?

The directrix x^2+8x+3 is y=-53/4

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directrix x^2+8x+3

directrix

x^{2} + 8 x + 3

y = - \frac{53}{4}

Solution steps

Rewrite

y = x^{2} + 8 x + 3

in the standard form

4 \cdot \frac{1}{4} (y - (- 13)) = (x - (- 4))^{2}

(h, k) = (- 4, - 13), 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

(- 4, - 13)

y-coordinate

y = - 13 - p

y = - 13 - \frac{1}{4}

Refine

y = - \frac{53}{4}

2 x^{2} - 2 x - 1

- x^{2} + 3 x + 7

(x - 6)^{2}

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

x = - \frac{( y + 3 ) ^{2}}{20} + 1