What is the directrix 4x^2-2x ?

The directrix 4x^2-2x is y=-5/16

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directrix 4x^2-2x

directrix

4 x^{2} - 2 x

y = - \frac{5}{16}

Solution steps

Rewrite

y = 4 x^{2} - 2 x

in the standard form

4 \cdot \frac{1}{16} (y - (- \frac{1}{4})) = (x - \frac{1}{4})^{2}

(h, k) = (\frac{1}{4}, - \frac{1}{4}), p = \frac{1}{16}

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{1}{4}, - \frac{1}{4})

y-coordinate

y = - \frac{1}{4} - p

y = - \frac{1}{4} - \frac{1}{16}

Refine

y = - \frac{5}{16}

y = - x^{2} + 18 x - 79

y = (x - 2)^{2} - 7

y > x^{2} - 3

x^{2} + 20 y = 10

2 y^{2} = - 3 x