What is the directrix-1/2 x^2+5x-2 ?

The directrix-1/2 x^2+5x-2 is y=11

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directrix-1/2 x^2+5x-2

directrix

- \frac{1}{2} x^{2} + 5 x - 2

y = 11

Solution steps

Rewrite

y = - \frac{1}{2} x^{2} + 5 x - 2

in the standard form

4 (- \frac{1}{2}) (y - \frac{21}{2}) = (x - 5)^{2}

(h, k) = (5, \frac{21}{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

(5, \frac{21}{2})

y-coordinate

y = \frac{21}{2} - p

y = \frac{21}{2} - (- \frac{1}{2})

Refine

y = 11

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

16 x^{2} - 25

- x^{2} + 64 x - 292

y = 5 x^{2} + 13 x - 6

y = 3 x^{2} + 6 x - 12