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vertices 9-x^2

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

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

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vertices −(x+3)²20 +1

Solution

Maximum (−3, 1)

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Find vertex using averaging the zeros

Find vertex using polynomial form

Find vertex using parabola form

Find vertex using vertex form

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y=−(x+3)²20 +1

Parabola equation in factored form

The vertex of an up-down facing parabola of the form y=a(x−m)(x−n) is the average of the zeros x_v=m+n2

y=−(x+3)²20 +1

The parabola parameters are:

a=−120 , m=2√5−3, n=−2√5−3

x_v=m+n2

x_v=(2√5−3)+(−2√5−3)2

Simplify (2√5−3)+(−2√5−3)2 : −3

x_v=−3

Plug in x_v=−3 to find the y_v value

y_v=1

Therefore the parabola vertex is

(−3, 1)

If a<0, then the vertex is a maximum value
If a>0, then the vertex is a minimum value
a=−120

Maximum (−3, 1)

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حل بواسطة: Find vertex using parabola form

حل بواسطة: Find vertex using vertex form

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

vertices 9-x^2

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