What is the directrix-2x^2-3x-1 ?

The directrix-2x^2-3x-1 is y= 1/4

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directrix-2x^2-3x-1

directrix

- 2 x^{2} - 3 x - 1

y = \frac{1}{4}

Solution steps

Rewrite

y = - 2 x^{2} - 3 x - 1

in the standard form

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

(h, k) = (- \frac{3}{4}, \frac{1}{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{1}{8})

y-coordinate

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

y = \frac{1}{8} - (- \frac{1}{8})

Refine

y = \frac{1}{4}

y = x^{2} - 6 x - 12

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

x^{2} - 8 x + \frac{63}{4}

x^{2} = - 2 y

\frac{1}{4} x^{2}