What is the directrix y= 1/2 x^2+9x+8 ?

The directrix y= 1/2 x^2+9x+8 is y=-33

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directrix y= 1/2 x^2+9x+8

directrix

y = \frac{1}{2} x^{2} + 9 x + 8

y = - 33

Solution steps

Rewrite

y = \frac{1}{2} x^{2} + 9 x + 8

in the standard form

4 \cdot \frac{1}{2} (y - (- \frac{65}{2})) = (x - (- 9))^{2}

(h, k) = (- 9, - \frac{65}{2}), p = \frac{1}{2}

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

(- 9, - \frac{65}{2})

y-coordinate

y = - \frac{65}{2} - p

y = - \frac{65}{2} - \frac{1}{2}

Refine

y = - 33

x = \frac{1}{4} y^{2}

y = - 3 (x + 2)^{2} + 5

y = 7 x^{2} - 3

- 0.0000005 x^{2} + 0.012 x + 19.21

4 y^{2} + x - 32 y + 68 = 0