What is the directrix 1/2 (x^2-4x+2) ?

The directrix 1/2 (x^2-4x+2) is y=-3/2

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directrix 1/2 (x^2-4x+2)

directrix

\frac{1}{2} (x^{2} - 4 x + 2)

y = - \frac{3}{2}

Solution steps

Rewrite

y = \frac{1}{2} (x^{2} - 4 x + 2)

in the standard form

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

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

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

(2, - 1)

y-coordinate

y = - 1 - p

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

Refine

y = - \frac{3}{2}

- x^{2} + 8 x - 7

y = x^{2} - 5 x + 4

y = x^{2} - x - 6

+ x^{2} + 12

y = 5 x^{2} + 210 x - 34775