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

The foci y=-2x+x(x-2)-2x(x-1)-(x-3) is (-3/2 ,5)

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

foci

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

(- \frac{3}{2}, 5)

Solution steps

Rewrite

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

in the standard form

4 (- \frac{1}{4}) (y - \frac{21}{4}) = (x - (- \frac{3}{2}))^{2}

(h, k) = (- \frac{3}{2}, \frac{21}{4}), p = - \frac{1}{4}

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

p

from the center

(- \frac{3}{2}, \frac{21}{4})

along the y-axis

(- \frac{3}{2}, \frac{21}{4} + p)

= (- \frac{3}{2}, \frac{21}{4} + (- \frac{1}{4}))

Refine

(- \frac{3}{2}, 5)

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

(y + 2)^{2} = - 16 (x + 5)

y^{2} + 4 x + 1 = 0

x = \frac{1}{12} y^{2}

x^{2} - 24 x - 12

What is the foci y=-2x+x(x-2)-2x(x-1)-(x-3) ?
The foci y=-2x+x(x-2)-2x(x-1)-(x-3) is (-3/2 ,5)