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