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

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

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directrix-2x^2+5x-6

directrix

- 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}

4 x^{2} - 20 x - 24 y + 97 = 0

\frac{6 x}{7} \frac{4 x}{3}

x^{2} - x - 6

y = (x + 4)^{2}

y = x^{2} + 2 x - 1 - (2 x^{2} - 3 x + 6)