What is the foci-16x^2+136x+57 ?

The foci-16x^2+136x+57 is (17/4 , 22143/64)

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foci-16x^2+136x+57

foci

- 16 x^{2} + 136 x + 57

(\frac{17}{4}, \frac{22143}{64})

Solution steps

Rewrite

y = - 16 x^{2} + 136 x + 57

in the standard form

4 (- \frac{1}{64}) (y - 346) = (x - \frac{17}{4})^{2}

(h, k) = (\frac{17}{4}, 346), p = - \frac{1}{64}

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

p

from the center

(\frac{17}{4}, 346)

along the y-axis

(\frac{17}{4}, 346 + p)

= (\frac{17}{4}, 346 + (- \frac{1}{64}))

Refine

(\frac{17}{4}, \frac{22143}{64})

2 x = - y^{2}

- x^{2} + 2 x - 6

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

x^{2} - 5 x 3

y = (x + 9) (x + 8)