Question

Постройте в одной системе координат графики функций: а)y=x в квадрате и y=(x+1) в квадрате

Answer 1

У = х² парабола, ветви направлены вверх, вершина параболы (0; 0). Точек пересечения с осью Ох нет. у=(х+1)² парабола, полученная из параболы у=х² сдвигом по оси Оу на 1 единицу вниз.

Answer 2

Graphing Functions in One Coordinate System

To graph the functions y = x^2 and y = (x + 1)^2 in one coordinate system, we can start by plotting the points and then connecting them to form the graphs.

The table of values for the functions is as follows:

| x | y = x^2 | | --- | ------- | | -2 | 4 | | -1 | 1 | | 0 | 0 | | 1 | 1 | | 2 | 4 |

| x | y = (x + 1)^2 | | --- | ------------ | | -2 | 1 | | -1 | 0 | | 0 | 1 | | 1 | 4 | | 2 | 9 |

Now, let's plot these points and connect them to form the graphs.

Graphs of the Functions

The graph of y = x^2 is a parabola that opens upwards, passing through the points (-2, 4), (-1, 1), (0, 0), (1, 1), and (2, 4).

The graph of y = (x + 1)^2 is also a parabola that opens upwards, passing through the points (-2, 1), (-1, 0), (0, 1), (1, 4), and (2, 9).

By plotting these points and connecting them, we can visualize the graphs of both functions in one coordinate system.

I hope this helps! If you have further questions or need additional assistance, feel free to ask.