What is the directrix 2x^2-1-(5x-6) ?

The directrix 2x^2-1-(5x-6) is y= 7/4

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directrix 2x^2-1-(5x-6)

directrix

2 x^{2} - 1 - (5 x - 6)

y = \frac{7}{4}

Solution steps

Rewrite

y = 2 x^{2} - 1 - (5 x - 6)

in the standard form

4 \cdot \frac{1}{8} (y - \frac{15}{8}) = (x - \frac{5}{4})^{2}

(h, k) = (\frac{5}{4}, \frac{15}{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{15}{8})

y-coordinate

y = \frac{15}{8} - p

y = \frac{15}{8} - \frac{1}{8}

Refine

y = \frac{7}{4}

y^{2} - 4 x - 4 = 0

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

y = - \frac{1}{12} x^{2} + x

y^{2} = 2 x

y = 6 x^{2} - 15 x