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Multi Var Functions Extreme Points Calculator

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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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Steps Examples

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directrix y=3x²−30x+77

Solution

y=2312

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Solve by:

Find vertex using polynomial form

Find vertex using parabola form

Find vertex using vertex form

Find vertex using averaging the zeros

One step at a time

y=x²−6x+8

Parabola equation in polynomial form

The vertex of an up-down facing parabola of the form y=ax²+bx+c is x_v=−b2a

The parabola parameters are:

a=1, b=−6, c=8

x_v=−b2a

x_v=−(−6)2· 1

بسّط

x_v=3

Plug in x_v=3 to find the y_v value

y_v=−1

لذلك رأس القطع المكافئ هو

(3, −1)

إذًا الرأس هو نقطة عظمى a<0 إذا تحقّق أنّ
إذًا الرأس هو نقطة صغرى a>0 إذا تحقّق أنّ
a=1

صغرى (3, −1)

Multi Var Functions Extreme Points Examples

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

Multi Var Functions Extreme Points Calculator

Solution

Solution steps

Number Line

Graph

1	−2
−2	0