Question

Question #b0cbf

Answer 1

`f(x)=(x-1)^2+4`
Minimum value is 4.

Explanation:

`f(x)=x^2-2x+1+4`
`f(x)=(x-1)^2+4`

The graph of this function is very similar to the graph of `f(x) = x^2`. `f(x)=(x-1)^2+4` would just be `f(x)=x^2` shifted one unit to the right and four units up.

The maximum/minimum point can be found using the vertex. Since the graph of this function faces up, you need to solve for the minimum point.

The vertex could be found by:
`x=-b/(2a)` where the function is expressed as `f(x)=ax^2+bx+c`.
`x=-(-2)/(2*1)`
`x=1`
`f(1)=4`
The minimum value is 4.