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

The directrix (1/2-x)(-1/2-x) is y=-1/2

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directrix (1/2-x)(-1/2-x)

directrix

(\frac{1}{2} - x) (- \frac{1}{2} - x)

y = - \frac{1}{2}

Solution steps

Rewrite

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

in the standard form

4 \cdot \frac{1}{4} (y - (- \frac{1}{4})) = (x - 0)^{2}

(h, k) = (0, - \frac{1}{4}), p = \frac{1}{4}

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

(0, - \frac{1}{4})

y-coordinate

y = - \frac{1}{4} - p

y = - \frac{1}{4} - \frac{1}{4}

Refine

y = - \frac{1}{2}

y = - 8 x^{2}

3 x^{2} - x

x^{2} + 14 x + 46

- 3 x^{2} + 17 x - 20

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