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vértices x^2+x+1

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vertices x²+x+1

Solution

Minimum (−12 , 34 )

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Find vertex using polynomial form

Find vertex using parabola form

Find vertex using vertex form

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y=x²+x+1

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=1, c=1

x_v=−b2a

x_v=−12· 1

Simplify

x_v=−12

Plug in x_v=−12 to find the y_v value

y_v=34

Therefore the parabola vertex is

(−12 , 34 )

If a<0, then the vertex is a maximum value
If a>0, then the vertex is a minimum value
a=1

Minimum (−12 , 34 )

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

vértices x^2+x+1

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