Question

What is the the vertex of `y = (x - 3)^2 + x^2-4x+3`?

Answer 1

`(2.5,-0.5) min`

Explanation:

`y'=2(x-3)*1+2x-4`
`=> 2x-6+2x-4`
`=> 4x-10`
`=> 2(2x-5)`

`y'=0`
`=>`
`2(2x-5)=0`
`=> 2x-5=0`
`=> 2x=5`
`=> x=5/2=2.5`

`y''=4>0 => min`

`y_((2.5))=(2.5-3)^2+(2.5)^2-4(2.5)+3=`
`=(-0.5)^2+(2.5)^2-10+3`
`=0.25+6.25-7`
`=-0.5`

`(2.5,-0.5) min`