What is the foci-2x^2+20x-52 ?

The foci-2x^2+20x-52 is (5,-17/8)

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foci-2x^2+20x-52

foci

- 2 x^{2} + 20 x - 52

(5, - \frac{17}{8})

Solution steps

Rewrite

y = - 2 x^{2} + 20 x - 52

in the standard form

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

(h, k) = (5, - 2), p = - \frac{1}{8}

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

p

from the center

(5, - 2)

along the y-axis

(5, - 2 + p)

= (5, - 2 + (- \frac{1}{8}))

Refine

(5, - \frac{17}{8})

x^{2} + 6 x + 9

+ x^{2} + 8 x - 80

x^{2} + 5 y = 14 x + 11

4 x^{2} + 16 x + 36

y = 4 x + 4 x - 2 + x^{2} - 3