What is the directrix y=x^2-9x+3 ?

The directrix y=x^2-9x+3 is y=-35/2

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directrix y=x^2-9x+3

directrix

y = x^{2} - 9 x + 3

y = - \frac{35}{2}

Solution steps

Rewrite

y = x^{2} - 9 x + 3

in the standard form

4 \cdot \frac{1}{4} (y - (- \frac{69}{4})) = (x - \frac{9}{2})^{2}

(h, k) = (\frac{9}{2}, - \frac{69}{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

(\frac{9}{2}, - \frac{69}{4})

y-coordinate

y = - \frac{69}{4} - p

y = - \frac{69}{4} - \frac{1}{4}

Refine

y = - \frac{35}{2}

- 2 x^{2} - 24 x - 54

x^{2} - 2 x - 3

y = (3 x - 7)^{2}

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

5 x^{2} - 15 x + 3