What is the directrix y=-2x^2+5x-6 ?

The directrix y=-2x^2+5x-6 is y=-11/4

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directrix y=-2x^2+5x-6

directrix

y = - 2 x^{2} + 5 x - 6

y = - \frac{11}{4}

Solution steps

Rewrite

y = - 2 x^{2} + 5 x - 6

in the standard form

4 (- \frac{1}{8}) (y - (- \frac{23}{8})) = (x - \frac{5}{4})^{2}

(h, k) = (\frac{5}{4}, - \frac{23}{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{5}{4}, - \frac{23}{8})

y-coordinate

y = - \frac{23}{8} - p

y = - \frac{23}{8} - (- \frac{1}{8})

Refine

y = - \frac{11}{4}

y^{2} + 2 x = 0

y = - (0.009 (x - 220)^{2} - 220)

y = x^{2} - 10 x - 24

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

- 2 x^{2} + 24 x + y - 70 = 0