To determine the least value of the given expression, set it equal to y.
Then, refer to the vertex form of parabola to get the minimum value y and at what value of x it occurs.
The vertex form is
`y=a(x-h)^2 + k`
where (h,k) is the vertex.
Note that the vertex is either the maximum or minimum point of the parabola. If a is positive, the vertex is the minimum point. If negative, it is the maximum point.
So, re-writing the given expression in vertex form results to:
By inspection, the vertex is (1,3). And since the value of a is positive2, then (1,3) is the minimum point.
Hence, the least value of `3+(x-1)^2` is 3 and it occurs at x=1.