What is the directrix x^2-6x+18 ?

The directrix x^2-6x+18 is y= 35/4

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directrix x^2-6x+18

directrix

x^{2} - 6 x + 18

y = \frac{35}{4}

Solution steps

Rewrite

y = x^{2} - 6 x + 18

in the standard form

4 \cdot \frac{1}{4} (y - 9) = (x - 3)^{2}

(h, k) = (3, 9), 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

(3, 9)

y-coordinate

y = 9 - p

y = 9 - \frac{1}{4}

Refine

y = \frac{35}{4}

(x - 3)^{2} = - 12 (y - 2)

3 x^{2} - 5

\frac{4 x ^{3} - 7 x ^{2} - 11 x + 5}{4 x + 5}

(\frac{1}{2} - x) (- \frac{1}{2} - x)

y = - 8 x^{2}