directrice y=3x^2-30x+77

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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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directrix y=3x²−30x+77

Solution

y=2312

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Parabola Directrix

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=3x²−30x+77 in the standard form

4· 112 (y−2)=(x−5)²

(h, k)=(5, 2), p=112

Parabola is symmetric around the y-axis and so the directrix is a line parallel to the x-axis, a distance −p from the center (5, 2) y-coordinate

y=2−p

y=2−112

Refine

y=2312

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

directrice y=3x^2-30x+77

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