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

The directrix x^2-4x+1 is y=-13/4

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directrix x^2-4x+1

directrix

x^{2} - 4 x + 1

y = - \frac{13}{4}

Solution steps

Rewrite

y = x^{2} - 4 x + 1

in the standard form

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

(h, k) = (2, - 3), 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, - 3)

y-coordinate

y = - 3 - p

y = - 3 - \frac{1}{4}

Refine

y = - \frac{13}{4}

y = - x^{2} - 6 x - 13

y = + x^{2} + 5

y = + x^{2} + 6

x^{2} + 12 x + 38

x = - 3 y^{2}