What is the directrix-x^2+6x-9 ?

The directrix-x^2+6x-9 is y= 1/4

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directrix-x^2+6x-9

directrix

- x^{2} + 6 x - 9

y = \frac{1}{4}

Solution steps

Rewrite

y = - x^{2} + 6 x - 9

in the standard form

4 (- \frac{1}{4}) (y - 0) = (x - 3)^{2}

(h, k) = (3, 0), 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, 0)

y-coordinate

y = 0 - p

y = 0 - (- \frac{1}{4})

Refine

y = \frac{1}{4}

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

x^{2} + 2 x + 1

x^{2} - 20 x + 100

y = 2 x^{2} + 4

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