What is the directrix x^2+5x-7 ?

The directrix x^2+5x-7 is y=-27/2

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directrix x^2+5x-7

directrix

x^{2} + 5 x - 7

y = - \frac{27}{2}

Solution steps

Rewrite

y = x^{2} + 5 x - 7

in the standard form

4 \cdot \frac{1}{4} (y - (- \frac{53}{4})) = (x - (- \frac{5}{2}))^{2}

(h, k) = (- \frac{5}{2}, - \frac{53}{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{5}{2}, - \frac{53}{4})

y-coordinate

y = - \frac{53}{4} - p

y = - \frac{53}{4} - \frac{1}{4}

Refine

y = - \frac{27}{2}

y^{2} - 6 y - 8 x - 23 = 0

t^{2}

4 x - 3 x^{2}

5 x^{2} + 7

(x + 1)^{2} = - 12 (y - 6)