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

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

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directrix y=x^2-4x+4

directrix

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

y = - \frac{1}{4}

Solution steps

Rewrite

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

in the standard form

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

(h, k) = (2, 0), 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

(2, 0)

y-coordinate

y = 0 - p

y = 0 - \frac{1}{4}

Refine

y = - \frac{1}{4}

5 x (2 x + 4) - 3 x

x^{2} + 12 y = 0

3 x^{2} - 30 x + 77

y = 2 x^{2} + 28 x + 105

(x - 1)^{2} = - 2 y - 11