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

The directrix 2x^2+x-3 is y=-13/4

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directrix 2x^2+x-3

directrix

2 x^{2} + x - 3

y = - \frac{13}{4}

Solution steps

Rewrite

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

in the standard form

4 \cdot \frac{1}{8} (y - (- \frac{25}{8})) = (x - (- \frac{1}{4}))^{2}

(h, k) = (- \frac{1}{4}, - \frac{25}{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{1}{4}, - \frac{25}{8})

y-coordinate

y = - \frac{25}{8} - p

y = - \frac{25}{8} - \frac{1}{8}

Refine

y = - \frac{13}{4}

y = x^{2} - 8 x + 7

y = \frac{x ( x + 5 )}{7}

x^{2} + 9 x + 20

y = - 7 x^{2} - 3

x^{2} - 10