What is the directrix y=x^2+2x-12 ?

The directrix y=x^2+2x-12 is y=-53/4

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directrix y=x^2+2x-12

directrix

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

y = - \frac{53}{4}

Solution steps

Rewrite

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

in the standard form

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

(h, k) = (- 1, - 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

(- 1, - 13)

y-coordinate

y = - 13 - p

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

Refine

y = - \frac{53}{4}

- 2 x^{2} + 24 x + y - 70 = 0

\frac{( 4 x + 5 ) ( 2 x + 3 )}{2}

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

- 2 - x + x^{2}

(x - 1)^{2} - 2