What is the directrix y=x^2+12x+45 ?

The directrix y=x^2+12x+45 is y= 35/4

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directrix y=x^2+12x+45

directrix

y = x^{2} + 12 x + 45

y = \frac{35}{4}

Solution steps

Rewrite

y = x^{2} + 12 x + 45

in the standard form

4 \cdot \frac{1}{4} (y - 9) = (x - (- 6))^{2}

(h, k) = (- 6, 9), 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

(- 6, 9)

y-coordinate

y = 9 - p

y = 9 - \frac{1}{4}

Refine

y = \frac{35}{4}

y = (5 x - 8)^{2}

y = 5 x^{2} + 6 x - 7

(x - 1)^{2} = - 6 (y + 4)

7 x^{2} + 70 x + 178

x^{2} - 6 x - 28 y = - 93