What is the directrix x^2-8x+24 ?

The directrix x^2-8x+24 is y= 31/4

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directrix x^2-8x+24

directrix

x^{2} - 8 x + 24

y = \frac{31}{4}

Solution steps

Rewrite

y = x^{2} - 8 x + 24

in the standard form

4 \cdot \frac{1}{4} (y - 8) = (x - 4)^{2}

(h, k) = (4, 8), 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

(4, 8)

y-coordinate

y = 8 - p

y = 8 - \frac{1}{4}

Refine

y = \frac{31}{4}

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

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

8 - 3 x - 2 x^{2}

(x + 2)^{2} = - 12 (y - 5)

y^{2} + 14 y + 4 x + 45 = 0