What is the directrix+2x^2+24x+76 ?

The directrix+2x^2+24x+76 is y= 31/8

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directrix+2x^2+24x+76

directrix

+ 2 x^{2} + 24 x + 76

y = \frac{31}{8}

Solution steps

Rewrite

y = 2 x^{2} + 24 x + 76

in the standard form

4 \cdot \frac{1}{8} (y - 4) = (x - (- 6))^{2}

(h, k) = (- 6, 4), p = \frac{1}{8}

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, 4)

y-coordinate

y = 4 - p

y = 4 - \frac{1}{8}

Refine

y = \frac{31}{8}

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

y^{2} + 2 x = 0

y = - (0.009 (x - 220)^{2} - 220)

y = x^{2} - 10 x - 24

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