Find the area of calculation of the function: y = 3x ^ 2 – 6x +1.
Apparently, there was a typo in the description of the assignment, or when translating the text of the assignment from another language into Russian, a phrase (“area of calculation”) was used that is not used in mathematical analysis.
If we are talking about the domain of definition D (y) of the function y = 3 * x ^ 2 – 6 * x + 1, then this function, as a particular form of a polynomial function (more precisely, as a quadratic function) or a polynomial (more precisely, a three-term) is defined in D (y) = (–∞; + ∞).
If we are talking about the range of values E (y) of a quadratic function y = 3 * x ^ 2 – 6 * x + 1, then such a problem can also be solved (there are various methods for finding the range of values of a quadratic function). Many solutions are based on the fact that the graph of a quadratic function is a parabola. For our example, the vertex of the parabola is the point (1; –2) on the coordinate plane Oxy and the branches of the parabola are directed upwards. Therefore, E (y) = [–2; + ∞).
Maybe it was necessary to determine the area of increase (and / or area of decrease) of the function y = 3 * x ^ 2 – 6 * x + 1. Please, the answer is ready (it was formed in item 3): function y = 3 * x ^ 2 – 6 * х + 1 decreases in the region (–∞; 1) and increases in (1; + ∞).
Surely enough to do fortune-telling. It seems that the compiler of the assignment has already found the answer to his question.