foci y=x^2-6x+8

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

☐²

x^☐

√☐

^□√☐

□□

log_□

θ

∞

∫

ddx

≥	≤	·	÷	`x`^◦	(☐)	\|☐\|	(`f` ◦ `g`)	`f`(`x`)	ln	`e`^☐
(☐)^′	∂∂`x`	∫_□^□	lim	∑	sin	cos	tan	cot	csc	sec

simplify solve for inverse tangent line

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foci y=x²−6x+8

Solution

(3, −34 )

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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=x²−6x+8 in the standard form

4· 14 (y−(−1))=(x−3)²

(h, k)=(3, −1), p=14

Parabola is symmetric around the y-axis and so the focus lies a distance p from the center (3, −1) along the y-axis

(3, −1+p)

=(3, −1+14 )

Refine

(3, −34 )

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

foci y=x^2-6x+8

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