Please help!!!
By completing the square in x^2-2x+3, find the minimum value of f(x)=x^2-2x+3

Question

Please help!!! 
By completing the square in x^2-2x+3, find the minimum value of f(x)=x^2-2x+3

hero · Answer

Do you really need to complete the square just to find the minimum value?

anonymous · Answer

yeah .

hero · Answer

Why not just simply use the vertex formula?

anonymous · Answer

I'm not finding the vertex.

hero · Answer

You're finding the minimum value of the function. To do that, use the formula for x coordinate of the vertex: 

$$x = -\frac{b}{2a}$$

hero · Answer

Then plug that value for x into the function, then find y coordinate.

anonymous · Answer

can you show me, I don't understand,

hero · Answer

$$x = -\frac{-2}{2(1)} = 1
\y = f(x)
\y = x^2 -2x + 3
\y = (1)^2 - 2(1) + 3
\y = 1 - 2 + 3
\ y = 3 + 1 - 2
\ y = 4 - 2
\y = 2$$

hero · Answer

Thus the minimum point is (1,2)

anonymous · Answer

Ohhhhh!! Thank Youu!!

hero · Answer

I hope you understand how to do these now.

zehanz · Answer

Completing the square:
f(x) = x^2-2x+3 =
(x-1)^2-1+3 =
(x-1)^2+2.
You can now see that this expression is minimal at x=1. 
The minimum is f(1) = 2.

hero · Answer

I was just showing her how to do it the easy way first.