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

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

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directrix y=x^2-4x+5

directrix

y = 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}

- 2 x^{2} - 3 x - 1

y = x^{2} - 6 x - 12

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

x^{2} - 8 x + \frac{63}{4}

x^{2} = - 2 y