What is the directrix x^2-4x+8 ?

The directrix x^2-4x+8 is y= 15/4

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directrix x^2-4x+8

directrix

x^{2} - 4 x + 8

y = \frac{15}{4}

Solution steps

Rewrite

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

in the standard form

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

(h, k) = (2, 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

(2, 4)

y-coordinate

y = 4 - p

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

Refine

y = \frac{15}{4}

2 x^{2} + 16 y = 0

y = 6 x^{2} - 29 x - 5

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

y = - 0.23 x^{2} + 1.87 x + 1.5

3 y^{2} = 24 x