What is the directrix y=x^2-15x ?

The directrix y=x^2-15x is y=-113/2

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directrix y=x^2-15x

directrix

y = x^{2} - 15 x

y = - \frac{113}{2}

Solution steps

Rewrite

y = x^{2} - 15 x

in the standard form

4 \cdot \frac{1}{4} (y - (- \frac{225}{4})) = (x - \frac{15}{2})^{2}

(h, k) = (\frac{15}{2}, - \frac{225}{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{15}{2}, - \frac{225}{4})

y-coordinate

y = - \frac{225}{4} - p

y = - \frac{225}{4} - \frac{1}{4}

Refine

y = - \frac{113}{2}

- x^{2} + 8 x - 10

y = - 4 x^{2} - 12 x - 8

x^{2} + 16 y = 0

y = 4 x^{2} - 24 x - 30

8 y = x^{2}