What is the directrix-x^2+64x-292 ?

The directrix-x^2+64x-292 is y= 2929/4

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directrix-x^2+64x-292

directrix

- x^{2} + 64 x - 292

y = \frac{2929}{4}

Solution steps

Rewrite

y = - x^{2} + 64 x - 292

in the standard form

4 (- \frac{1}{4}) (y - 732) = (x - 32)^{2}

(h, k) = (32, 732), 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

(32, 732)

y-coordinate

y = 732 - p

y = 732 - (- \frac{1}{4})

Refine

y = \frac{2929}{4}

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

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

(x - 5)^{2} = 20 (y - 5)

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

x = + \frac{17}{4} (y + 2)^{2}