Find the least value of   `3+(x-1)^2` . State the value of x for which it occurs.

Expert Answers
lemjay eNotes educator| Certified Educator

To determine the least value of the given expression, set it equal to y.

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

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.