What is the directrix y=x^2+7x-3 ?

The directrix y=x^2+7x-3 is y=-31/2

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directrix y=x^2+7x-3

directrix

y = x^{2} + 7 x - 3

y = - \frac{31}{2}

Solution steps

Rewrite

y = x^{2} + 7 x - 3

in the standard form

4 \cdot \frac{1}{4} (y - (- \frac{61}{4})) = (x - (- \frac{7}{2}))^{2}

(h, k) = (- \frac{7}{2}, - \frac{61}{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{7}{2}, - \frac{61}{4})

y-coordinate

y = - \frac{61}{4} - p

y = - \frac{61}{4} - \frac{1}{4}

Refine

y = - \frac{31}{2}

y^{2} + 12 x - 2 y - 11 = 0

\frac{x ^{2}}{9}

x^{2} + 36

y^{2} - 12 x - 2 y - 25 = 0

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