What is the foci-(x^2)/8+x/4+23/8 ?

The foci-(x^2)/8+x/4+23/8 is (1,1)

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foci-(x^2)/8+x/4+23/8

foci

- \frac{x ^{2}}{8} + \frac{x}{4} + \frac{23}{8}

(1, 1)

Solution steps

Rewrite

y = - \frac{x ^{2}}{8} + \frac{x}{4} + \frac{23}{8}

in the standard form

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

(h, k) = (1, 3), p = - 2

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

p

from the center

(1, 3)

along the y-axis

(1, 3 + p)

= (1, 3 + (- 2))

Refine

(1, 1)

3 x^{2} + 8

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

(x + 3)^{2} - 8

- x^{2} + 3 x

y = 4 x^{2} + 8 x - 11