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foci y=x^2+2x-1-(2x^2-3x+6)

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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−1−(2x²−3x+6)

Solution

(52 , −1)

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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−1−(2x²−3x+6) in the standard form

4(−14 )(y−(−34 ))=(x−52 )²

(h, k)=(52 , −34 ), p=−14

Parabola is symmetric around the y-axis and so the focus lies a distance p from the center (52 , −34 ) along the y-axis

(52 , −34 +p)

=(52 , −34 +(−14 ))

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(52 , −1)

Order of operations three/four steps with parentheses Examples

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

foci y=x^2+2x-1-(2x^2-3x+6)

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