What is the foci-(x+5)^2+6 ?

The foci-(x+5)^2+6 is (-5, 23/4)

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foci-(x+5)^2+6

foci

- (x + 5)^{2} + 6

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

Solution steps

Rewrite

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

in the standard form:

4 (- \frac{1}{4}) (y - 6) = (x - (- 5))^{2}

(h, k) = (- 5, 6), p = - \frac{1}{4}

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

p

from the center

(- 5, 6)

along the y-axis

(- 5, 6 + p)

= (- 5, 6 + (- \frac{1}{4}))

Refine

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

y = x^{2} + 3 x - 5

x^{2} + 2 x - 7

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

y = + 5 - x^{2}

y = (0.5 - x)^{2}