What is the directrix y=x^2-8x ?

The directrix y=x^2-8x is y=-65/4

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directrix y=x^2-8x

directrix

y = x^{2} - 8 x

y = - \frac{65}{4}

Solution steps

Rewrite

y = x^{2} - 8 x

in the standard form

4 \cdot \frac{1}{4} (y - (- 16)) = (x - 4)^{2}

(h, k) = (4, - 16), 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, - 16)

y-coordinate

y = - 16 - p

y = - 16 - \frac{1}{4}

Refine

y = - \frac{65}{4}

- x^{2} - 4 x + 2

y = x^{2} - 6 x

y^{2} + 4 x = 0

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

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