What is the directrix 2x^2-2x-1 ?

The directrix 2x^2-2x-1 is y=-13/8

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directrix 2x^2-2x-1

directrix

2 x^{2} - 2 x - 1

y = - \frac{13}{8}

Solution steps

Rewrite

y = 2 x^{2} - 2 x - 1

in the standard form

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

(h, k) = (\frac{1}{2}, - \frac{3}{2}), 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{1}{2}, - \frac{3}{2})

y-coordinate

y = - \frac{3}{2} - p

y = - \frac{3}{2} - \frac{1}{8}

Refine

y = - \frac{13}{8}

- x^{2} + 3 x + 7

(x - 6)^{2}

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

x = - \frac{( y + 3 ) ^{2}}{20} + 1

2 x^{2} - 4