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

The directrix y=2x^2-3x is y=-5/4

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directrix y=2x^2-3x

directrix

y = 2 x^{2} - 3 x

y = - \frac{5}{4}

Solution steps

Rewrite

y = 2 x^{2} - 3 x

in the standard form

4 \cdot \frac{1}{8} (y - (- \frac{9}{8})) = (x - \frac{3}{4})^{2}

(h, k) = (\frac{3}{4}, - \frac{9}{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{3}{4}, - \frac{9}{8})

y-coordinate

y = - \frac{9}{8} - p

y = - \frac{9}{8} - \frac{1}{8}

Refine

y = - \frac{5}{4}

2 x^{2} - 2

2 x^{2} + 3

x^{2} + x + 1

4 + 2 x - x^{2}

\frac{1}{4} x^{2} + x - 8