What is the directrix y=x^2-2x+5 ?

The directrix y=x^2-2x+5 is y= 15/4

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directrix y=x^2-2x+5

directrix

y = x^{2} - 2 x + 5

y = \frac{15}{4}

Solution steps

Rewrite

y = x^{2} - 2 x + 5

in the standard form

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

(h, k) = (1, 4), 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, 4)

y-coordinate

y = 4 - p

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

Refine

y = \frac{15}{4}

y = - 3 x^{2} + 6 x - 1

X^{2} - 5 X - 24

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

y^{2} + 4 y + 8 x - 12 = 0

4 x^{2} - 8 x + 2 y = 5