What is the directrix y=2x^2-7x-3 ?

The directrix y=2x^2-7x-3 is y=-37/4

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directrix y=2x^2-7x-3

directrix

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

y = - \frac{37}{4}

Solution steps

Rewrite

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

in the standard form

4 \cdot \frac{1}{8} (y - (- \frac{73}{8})) = (x - \frac{7}{4})^{2}

(h, k) = (\frac{7}{4}, - \frac{73}{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{7}{4}, - \frac{73}{8})

y-coordinate

y = - \frac{73}{8} - p

y = - \frac{73}{8} - \frac{1}{8}

Refine

y = - \frac{37}{4}

x^{2} + 5 x - 7

y^{2} - 6 y - 8 x - 23 = 0

t^{2}

4 x - 3 x^{2}

5 x^{2} + 7