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vertex y=x^2+2x+3

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vertices y=x²+2x+3

Solution

Minimum (−1, 2)

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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+2x+3

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=2, c=3

x_v=−b2a

x_v=−22· 1

Simplify

x_v=−1

Plug in x_v=−1 to find the y_v value

y_v=2

Therefore the parabola vertex is

(−1, 2)

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

Minimum (−1, 2)

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

vertex y=x^2+2x+3

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