What is the foci-2x^2+6x-3 ?

The foci-2x^2+6x-3 is (3/2 , 11/8)

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foci-2x^2+6x-3

foci

- 2 x^{2} + 6 x - 3

(\frac{3}{2}, \frac{11}{8})

Solution steps

Rewrite

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

in the standard form

4 (- \frac{1}{8}) (y - \frac{3}{2}) = (x - \frac{3}{2})^{2}

(h, k) = (\frac{3}{2}, \frac{3}{2}), p = - \frac{1}{8}

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

p

from the center

(\frac{3}{2}, \frac{3}{2})

along the y-axis

(\frac{3}{2}, \frac{3}{2} + p)

= (\frac{3}{2}, \frac{3}{2} + (- \frac{1}{8}))

Refine

(\frac{3}{2}, \frac{11}{8})

y = 6 x^{2} - 29 x - 5

y = 1 - 3 x - x^{2}

x^{2} - 2 x - 4 y + 13 = 0

2 y^{2} - 16 y + 72 = 20 x

y^{2} + 4 x - 8 y + 12 = 0