What is the directrix y=x^2-3x-4 ?

The directrix y=x^2-3x-4 is y=-13/2

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directrix y=x^2-3x-4

directrix

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

y = - \frac{13}{2}

Solution steps

Rewrite

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

in the standard form

4 \cdot \frac{1}{4} (y - (- \frac{25}{4})) = (x - \frac{3}{2})^{2}

(h, k) = (\frac{3}{2}, - \frac{25}{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{3}{2}, - \frac{25}{4})

y-coordinate

y = - \frac{25}{4} - p

y = - \frac{25}{4} - \frac{1}{4}

Refine

y = - \frac{13}{2}

- 2 x^{2} + 4

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

x - y^{2} = 0

9 x^{2} - 4

- x^{2} + 8 x - 15