What is the directrix y=x^2+5x+6 ?

The directrix y=x^2+5x+6 is y=-1/2

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directrix y=x^2+5x+6

directrix

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

y = - \frac{1}{2}

Solution steps

Rewrite

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

in the standard form

4 \cdot \frac{1}{4} (y - (- \frac{1}{4})) = (x - (- \frac{5}{2}))^{2}

(h, k) = (- \frac{5}{2}, - \frac{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

(- \frac{5}{2}, - \frac{1}{4})

y-coordinate

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

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

Refine

y = - \frac{1}{2}

y^{2} = 6 x

- 4 x^{2} + 2 x + 2

(y - 2)^{2} = 8 (x - 1)

y = 4 x + 4 x - 2 + x^{2} - 3

y = - 5 x^{2} + 118 x + 7