What is the directrix x^2+5x-84 ?

The directrix x^2+5x-84 is y=-181/2

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directrix x^2+5x-84

directrix

x^{2} + 5 x - 84

y = - \frac{181}{2}

Solution steps

Rewrite

y = x^{2} + 5 x - 84

in the standard form

4 \cdot \frac{1}{4} (y - (- \frac{361}{4})) = (x - (- \frac{5}{2}))^{2}

(h, k) = (- \frac{5}{2}, - \frac{361}{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{361}{4})

y-coordinate

y = - \frac{361}{4} - p

y = - \frac{361}{4} - \frac{1}{4}

Refine

y = - \frac{181}{2}

2 x^{2} - 32 x - y + 127 = 0

y^{2} + 2 x + 6 y + 17 = 0

(x - 7)^{2}

- 3 x^{2} + 75

y = \frac{95 x ^{2} - 10 x + 26}{10}