What is the foci y=-2x^2+5x-6 ?

The foci y=-2x^2+5x-6 is (5/4 ,-3)

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foci y=-2x^2+5x-6

foci

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

(\frac{5}{4}, - 3)

Solution steps

Rewrite

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

in the standard form

4 (- \frac{1}{8}) (y - (- \frac{23}{8})) = (x - \frac{5}{4})^{2}

(h, k) = (\frac{5}{4}, - \frac{23}{8}), p = - \frac{1}{8}

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

p

from the center

(\frac{5}{4}, - \frac{23}{8})

along the y-axis

(\frac{5}{4}, - \frac{23}{8} + p)

= (\frac{5}{4}, - \frac{23}{8} + (- \frac{1}{8}))

Refine

(\frac{5}{4}, - 3)

x^{2} + 8 x - 5

12 x^{2} + 12 x + 1

- x^{2} + 8 x - 13

x^{2} = - 9 y

+ 4 t^{2}