What is the foci-3x^2+8x+896 ?

The foci-3x^2+8x+896 is (4/3 , 3605/4)

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foci-3x^2+8x+896

foci

- 3 x^{2} + 8 x + 896

(\frac{4}{3}, \frac{3605}{4})

Solution steps

Rewrite

y = - 3 x^{2} + 8 x + 896

in the standard form

4 (- \frac{1}{12}) (y - \frac{2704}{3}) = (x - \frac{4}{3})^{2}

(h, k) = (\frac{4}{3}, \frac{2704}{3}), p = - \frac{1}{12}

Parabola is symmetric around the y-axis and so the focus lies a distance

p

from the center

(\frac{4}{3}, \frac{2704}{3})

along the y-axis

(\frac{4}{3}, \frac{2704}{3} + p)

= (\frac{4}{3}, \frac{2704}{3} + (- \frac{1}{12}))

Refine

(\frac{4}{3}, \frac{3605}{4})

x^{2} + 36

y = \frac{40 x ^{3}}{3 x}

x^{2} + 10 x - 2 y + 21 = 0

y = 6 x^{2} + 5 x + 7

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