Find the smallest function value y = x ^ 2-18x + 3

We have a function:

y = x ^ 2 – 18 * x + 3.

The function is quadratic. The graph is a parabola, the branches of which are directed upwards.

To find the smallest value of the function, we select the square of the binomial, thereby determining the coordinates of the vertex of the parabola:

x ^ 2 – 18 * x + 3 = x ^ 2 – 2 * x * 9 + 9 ^ 2 – 78 = (x – 9) ^ 2 – 78.

The function takes its minimum value at x = 9:

y (9) = -78.