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foci y=x^2-2x-3

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`x`²	`x`^□	log_□	√☐	^□√☐	≤	≥	□□	·	÷	`x`^◦	π
(☐)^′	`ddx`	∂∂`x`	∫	∫_□^□	lim	∑	∞	`θ`	(`f` ◦ `g`)	`f`(`x`)

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foci y=x²−2x−3

Solution

(1, −154 )

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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=x²−2x−3 in the standard form

4· 14 (y−(−4))=(x−1)²

(h, k)=(1, −4), p=14

Parabola is symmetric around the y-axis and so the focus lies a distance p from the center (1, −4) along the y-axis

(1, −4+p)

=(1, −4+14 )

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(1, −154 )

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

foci y=x^2-2x-3

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