What is the directrix 2x^2+8x+13 ?

The directrix 2x^2+8x+13 is y= 39/8

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directrix 2x^2+8x+13

directrix

2 x^{2} + 8 x + 13

y = \frac{39}{8}

Solution steps

Rewrite

y = 2 x^{2} + 8 x + 13

in the standard form

4 \cdot \frac{1}{8} (y - 5) = (x - (- 2))^{2}

(h, k) = (- 2, 5), 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

(- 2, 5)

y-coordinate

y = 5 - p

y = 5 - \frac{1}{8}

Refine

y = \frac{39}{8}

2 x^{2} - 4 x + 9

3 x^{2} - 31 x + 56 - (x - 8)

y = - 2.1 x^{2} + 410 x - 1340

y = x^{2} - 10000 x - 24000000

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