What is the directrix y=2x^2-13x-7 ?

The directrix y=2x^2-13x-7 is y=-113/4

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directrix y=2x^2-13x-7

directrix

y = 2 x^{2} - 13 x - 7

y = - \frac{113}{4}

Solution steps

Rewrite

y = 2 x^{2} - 13 x - 7

in the standard form

4 \cdot \frac{1}{8} (y - (- \frac{225}{8})) = (x - \frac{13}{4})^{2}

(h, k) = (\frac{13}{4}, - \frac{225}{8}), 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

(\frac{13}{4}, - \frac{225}{8})

y-coordinate

y = - \frac{225}{8} - p

y = - \frac{225}{8} - \frac{1}{8}

Refine

y = - \frac{113}{4}

x = 7 y^{2}

y = 7 x^{2} - 9 x - 5

y = 3 x^{2} - 5 x 7

x^{2} - 4 x + 8

2 x^{2} + 16 y = 0