What is the foci y=-x^2+64x-292 ?

The foci y=-x^2+64x-292 is (32, 2927/4)

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foci y=-x^2+64x-292

foci

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

(32, \frac{2927}{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 focus lies a distance

p

from the center

(32, 732)

along the y-axis

(32, 732 + p)

= (32, 732 + (- \frac{1}{4}))

Refine

(32, \frac{2927}{4})

y = x^{2} - 12 x + 5

y = - 2 x + x (x - 2) - 2 x (x - 1) - (x - 3)

(y - 2)^{2} = 8 (x - 1)

(y + 2)^{2} = - 16 (x + 5)

y^{2} + 4 x + 1 = 0