What is the directrix y=7x^2-9x-5 ?

The directrix y=7x^2-9x-5 is y=-111/14

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directrix y=7x^2-9x-5

directrix

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

y = - \frac{111}{14}

Solution steps

Rewrite

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

in the standard form

4 \cdot \frac{1}{28} (y - (- \frac{221}{28})) = (x - \frac{9}{14})^{2}

(h, k) = (\frac{9}{14}, - \frac{221}{28}), p = \frac{1}{28}

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{9}{14}, - \frac{221}{28})

y-coordinate

y = - \frac{221}{28} - p

y = - \frac{221}{28} - \frac{1}{28}

Refine

y = - \frac{111}{14}

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

x^{2} - 4 x + 8

2 x^{2} + 16 y = 0

y = 6 x^{2} - 29 x - 5

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