What is the directrix y=x^2-4x+3 ?

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

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directrix y=x^2-4x+3

directrix

y = x^{2} - 4 x + 3

y = - \frac{5}{4}

Solution steps

Rewrite

y = x^{2} - 4 x + 3

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{5}{4}

(x - 2)^{2} = 8 (y - 1)

- x^{2} + 6 x - 9

(x + 3)^{2} = 24 (y - 1)

x^{2} + 2 x + 1

x^{2} - 20 x + 100