What is the foci y=(x+1/4)(x-5) ?

The foci y=(x+1/4)(x-5) is (19/8 ,-425/64)

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foci y=(x+1/4)(x-5)

foci

y = (x + \frac{1}{4}) (x - 5)

(\frac{19}{8}, - \frac{425}{64})

Solution steps

Rewrite

y = (x + \frac{1}{4}) (x - 5)

in the standard form

4 \cdot \frac{1}{4} (y - (- \frac{441}{64})) = (x - \frac{19}{8})^{2}

(h, k) = (\frac{19}{8}, - \frac{441}{64}), p = \frac{1}{4}

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

p

from the center

(\frac{19}{8}, - \frac{441}{64})

along the y-axis

(\frac{19}{8}, - \frac{441}{64} + p)

= (\frac{19}{8}, - \frac{441}{64} + \frac{1}{4})

Refine

(\frac{19}{8}, - \frac{425}{64})

y^{2} - 16 x = 0

6 x^{2}

y = 2 (x + 1)^{2}

2 x^{2} - 4 x + 9

y = 5 x^{2} + 210 x - 34775