The function is given. y = x ^ 2-4x + 3. Find the value of x at which the function takes the smallest value.

A function is given y = x ^ 2 – 4 * x + 3.

Let’s find its smallest value.

You can solve the problem graphically – draw a graph of the function and find the “lowest” point, and take its ordinate.

You can find the coordinates of the vertex of the point and take its ordinate, since the branches are directed upward at the parabola.

We transform the function formula:

x ^ 2 – 4 * x + 3 = x ^ 2 – 2 * x * 2 + 2 ^ 2 – 1 = (x – 2) ^ 2 – 1.

y = (x – 2) ^ 2 – 1.

The square of any number is a non-negative number, the smallest value of the expression we get when the square of the number takes its minimum value – zero.

When x = 2, y = -1 is the minimum value of the function.