What is the directrix-1/2 x^2+7x-3 ?

The directrix-1/2 x^2+7x-3 is y=22

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directrix-1/2 x^2+7x-3

directrix

- \frac{1}{2} x^{2} + 7 x - 3

y = 22

Solution steps

Rewrite

y = - \frac{1}{2} x^{2} + 7 x - 3

in the standard form

4 (- \frac{1}{2}) (y - \frac{43}{2}) = (x - 7)^{2}

(h, k) = (7, \frac{43}{2}), p = - \frac{1}{2}

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

(7, \frac{43}{2})

y-coordinate

y = \frac{43}{2} - p

y = \frac{43}{2} - (- \frac{1}{2})

Refine

y = 22

y = - 3 x^{2} + 12 x - 4

y = x^{2} - 2 x + 8

4 y^{2} - 48 x - 20 y = 71

y = (2 x + 5)^{2}

y = (x - 4)^{2} + 2