What is the directrix y=2x^2-6x+4 ?

The directrix y=2x^2-6x+4 is y=-5/8

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directrix y=2x^2-6x+4

directrix

y = 2 x^{2} - 6 x + 4

y = - \frac{5}{8}

Solution steps

Rewrite

y = 2 x^{2} - 6 x + 4

in the standard form

4 \cdot \frac{1}{8} (y - (- \frac{1}{2})) = (x - \frac{3}{2})^{2}

(h, k) = (\frac{3}{2}, - \frac{1}{2}), 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{3}{2}, - \frac{1}{2})

y-coordinate

y = - \frac{1}{2} - p

y = - \frac{1}{2} - \frac{1}{8}

Refine

y = - \frac{5}{8}

\frac{( x - 5 ) ( x - 10 )}{50}

2 x^{2} - 12 x + 14 - 14 y = 0

(4 - x)^{2}

y = 7 x^{2}

x = (\frac{4}{5} - 3 y) \cdot (\frac{4}{5} + 3 y)