What is the directrix y=2x^2-10x+12 ?

The directrix y=2x^2-10x+12 is y=-5/8

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directrix y=2x^2-10x+12

directrix

y = 2 x^{2} - 10 x + 12

y = - \frac{5}{8}

Solution steps

Rewrite

y = 2 x^{2} - 10 x + 12

in the standard form

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

(h, k) = (\frac{5}{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{5}{2}, - \frac{1}{2})

y-coordinate

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

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

Refine

y = - \frac{5}{8}

- x^{2} + 14 x - 45

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

y^{2} = 6 x

- 4 x^{2} + 2 x + 2

(y - 2)^{2} = 8 (x - 1)