What is the directrix x^2+3x-4 ?

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

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directrix x^2+3x-4

directrix

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}

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

5 x (2 x + 4) - 3 x

x^{2} + 12 y = 0

3 x^{2} - 30 x + 77

y = 2 x^{2} + 28 x + 105