What is the directrix y=x^2-6x ?

The directrix y=x^2-6x is y=-37/4

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directrix y=x^2-6x

directrix

y = x^{2} - 6 x

y = - \frac{37}{4}

Solution steps

Rewrite

y = x^{2} - 6 x

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{37}{4}

y^{2} + 4 x = 0

y^{2} = \frac{- 16}{5} x

y = (2 X + 5) (3 X - 7)

(y + 2)^{2} = - 16 (x + 9)

x^{2} + 5 x - 84