What is the directrix y=x^2-2x+8 ?

The directrix y=x^2-2x+8 is y= 27/4

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directrix y=x^2-2x+8

directrix

y = x^{2} - 2 x + 8

y = \frac{27}{4}

Solution steps

Rewrite

y = x^{2} - 2 x + 8

in the standard form

4 \cdot \frac{1}{4} (y - 7) = (x - 1)^{2}

(h, k) = (1, 7), 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, 7)

y-coordinate

y = 7 - p

y = 7 - \frac{1}{4}

Refine

y = \frac{27}{4}

4 y^{2} - 48 x - 20 y = 71

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

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

4 t - 9 t^{2}

y = (x + 2)^{2} - 3