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focos y=(-3x^2-2x+6)/5

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foci y=−3x²−2x+65

Solution

(−13 , 1720 )

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Parabola Focus

A parabola is the locus of points such that the distance to a point (the focus) equals the distance to a line (the directrix)

Parabola standard equation

4p(y−k)=(x−h)² is the standard equation for an up-down facing parabola with vertex at (h, k),
and a focal length |p|

Rewrite y=−3x²−2x+65 in the standard form

4(−512 )(y−1915 )=(x−(−13 ))²

(h, k)=(−13 , 1915 ), p=−512

Parabola is symmetric around the y-axis and so the focus lies a distance p from the center (−13 , 1915 ) along the y-axis

(−13 , 1915 +p)

=(−13 , 1915 +(−512 ))

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(−13 , 1720 )

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−▭▭	<	7	8	9	÷	`AC`
+▭▭	>	4	5	6	×	☐☐☐
×▭▭	(	1	2	3	−	`x`
▭ \|▭	)	.	0	=	+	`y`

focos y=(-3x^2-2x+6)/5

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