Question

Надо построить график функции y= -(x-2)² . Укажите промежутки возрастания и убывания функции.

Answer 1

Ответ не знаю а график должно было быть такой) 

Answer 2

Graph of the Function y = -(x-2)²

To graph the function y = -(x-2)², we can start by identifying the key features of the function. The function is a quadratic function, and its graph will be a parabola. The negative sign in front of the function means that the parabola will be reflected in the x-axis.

The vertex of the parabola can be found using the formula for the vertex of a parabola, which is given by (h, k) where h is the x-coordinate and k is the y-coordinate. In this case, the vertex is at (2, 0) because the function is in the form y = a(x - h)² + k, where (h, k) is the vertex.

Now, let's identify the intervals of increase and decrease for the function.

Intervals of Increase and Decrease

The function y = -(x-2)² is a downward-facing parabola, and therefore, it decreases as x increases and increases as x decreases. The vertex of the parabola is at (2, 0), and the parabola opens downwards. Therefore, the function decreases for x values less than 2 and increases for x values greater than 2.

So, the interval of decrease is (-∞, 2), and the interval of increase is (2, +∞).

Now, let's summarize the information about the function and its intervals of increase and decrease.

The graph of the function y = -(x-2)² is a downward-facing parabola with the vertex at (2, 0). The function decreases for x values in the interval (-∞, 2) and increases for x values in the interval (2, +∞).

I hope this helps! If you have any further questions, feel free to ask.