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

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

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directrix x^2-2x+2

directrix

x^{2} - 2 x + 2

y = \frac{3}{4}

Solution steps

Rewrite

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

in the standard form

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

(h, k) = (1, 1), 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

(1, 1)

y-coordinate

y = 1 - p

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

Refine

y = \frac{3}{4}

- x^{2} - 3 x - 2

y = x^{2} + 7 x - 3

y^{2} + 12 x - 2 y - 11 = 0

\frac{x ^{2}}{9}

x^{2} + 36