Question

Sam completed the square for the quadratic equation y=1/2x^2−2x+3 in order to determine the minimum value of the equation, as shown.

Answer 1

`(2,1)`

Explanation:

You can just use the formula
`x=-(b)/(2a)`:

`y=ax^2+bx+c`

`y=(1)/(2)x^2-2x+3`

`x=-(-2)/(2((1)/(2)))=(2)/(1)=2`

`y=(1)/(2)(2)^2-2(2)+3=(1)/(2)(4)-4+3=2-4+3=-2+3=1`

Therefore, the minimum value of the equation is
`(2,1)`