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

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

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directrix 2x^2-13x-7

directrix

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}

\frac{x ^{2} x ^{1}}{x}

(x + 1)^{2}

2 y^{2} + x + 20 y + 51 = 0

- 8 (x - 5) = (y + 1)^{2}

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