What is the foci 3(x-1)(x+2) ?

The foci 3(x-1)(x+2) is (-1/2 ,-20/3)

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foci 3(x-1)(x+2)

foci

3 (x - 1) (x + 2)

(- \frac{1}{2}, - \frac{20}{3})

Solution steps

Rewrite

y = 3 (x - 1) (x + 2)

in the standard form

4 \cdot \frac{1}{12} (y - (- \frac{27}{4})) = (x - (- \frac{1}{2}))^{2}

(h, k) = (- \frac{1}{2}, - \frac{27}{4}), p = \frac{1}{12}

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

p

from the center

(- \frac{1}{2}, - \frac{27}{4})

along the y-axis

(- \frac{1}{2}, - \frac{27}{4} + p)

= (- \frac{1}{2}, - \frac{27}{4} + \frac{1}{12})

Refine

(- \frac{1}{2}, - \frac{20}{3})

3 x^{2} - 9 x

9 - x^{2}

+ (5 x - 1)^{2}

y = x^{2} + 2 x + 12

x = (y + 4)^{2}