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

The directrix-x^2+3x+7 is y= 19/2

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directrix-x^2+3x+7

directrix

y = \frac{19}{2}

Solution steps

Rewrite

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

in the standard form

4 (- \frac{1}{4}) (y - \frac{37}{4}) = (x - \frac{3}{2})^{2}

(h, k) = (\frac{3}{2}, \frac{37}{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{37}{4})

y-coordinate

y = \frac{37}{4} - p

y = \frac{37}{4} - (- \frac{1}{4})

Refine

y = \frac{19}{2}