What is the directrix (x(x+5))/7 ?

The directrix (x(x+5))/7 is y=-37/14

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directrix (x(x+5))/7

directrix

y = - \frac{37}{14}

Solution steps

Rewrite

y = \frac{x ( x + 5 )}{7}

in the standard form

4 \cdot \frac{7}{4} (y - (- \frac{25}{28})) = (x - (- \frac{5}{2}))^{2}

(h, k) = (- \frac{5}{2}, - \frac{25}{28}), p = \frac{7}{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{25}{28})

y-coordinate

y = - \frac{25}{28} - p

y = - \frac{25}{28} - \frac{7}{4}

Refine

y = - \frac{37}{14}