What is the directrix y=2x^2+9x-3 ?

The directrix y=2x^2+9x-3 is y=-53/4

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directrix y=2x^2+9x-3

directrix

y = 2 x^{2} + 9 x - 3

y = - \frac{53}{4}

Solution steps

Rewrite

y = 2 x^{2} + 9 x - 3

in the standard form

4 \cdot \frac{1}{8} (y - (- \frac{105}{8})) = (x - (- \frac{9}{4}))^{2}

(h, k) = (- \frac{9}{4}, - \frac{105}{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{9}{4}, - \frac{105}{8})

y-coordinate

y = - \frac{105}{8} - p

y = - \frac{105}{8} - \frac{1}{8}

Refine

y = - \frac{53}{4}

y = x^{2} + 8 x - 5

(y - 0)^{2} = - 43 (x - 0)

y = x^{2} + 22

- 29 x^{2} + 1388 x - 10040

x = - 2 y^{2}