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

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

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directrix y=-x^2+2x-2

directrix

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

y = - \frac{3}{4}

Solution steps

Rewrite

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

in the standard form

4 (- \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} - 8 x + \frac{63}{4}

x^{2} = - 2 y

\frac{1}{4} x^{2}

3 y^{2} - 30 y + 77

(x - 3)^{2} + 1