What is the directrix x^2-4x+5 ?

The directrix x^2-4x+5 is y= 3/4

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directrix x^2-4x+5

directrix

x^{2} - 4 x + 5

y = \frac{3}{4}

Solution steps

Rewrite

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

in the standard form

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

(h, k) = (2, 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

(2, 1)

y-coordinate

y = 1 - p

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

Refine

y = \frac{3}{4}

y = \frac{1}{2} x^{2} + 9 x + 8

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

y = - 3 (x + 2)^{2} + 5

y = 7 x^{2} - 3

- 0.0000005 x^{2} + 0.012 x + 19.21