Question

Построить график функции х+у²=0. И это странно, ведь тогда у²=-х а этого быть не может....тогда как?

Answer 1

Строим график ф-ии:

$y=\sqrt{-x};\ \ \ \ x\leq0$

См. приложение.

Взял только положительную ветвь корня, так как задание для 5-9 классов.

Вообще это уравнение параболы, расположенной вдоль оси Х - ветвями влево

Answer 2

Graph of the Function x * y^2 = 0

To graph the function x * y^2 = 0, we can start by understanding the nature of this equation. The equation x * y^2 = 0 can be broken down into two separate equations: x = 0 and y^2 = 0.

1. x = 0: This represents a vertical line passing through the y-axis at x = 0. 2. y^2 = 0: This represents a horizontal line at y = 0.

When we combine these two equations, we find that the graph of the function x * y^2 = 0 consists of the y-axis (x = 0) and the x-axis (y = 0).

Understanding the Equation y^2 = -x

The statement "у² = -х" suggests the equation y^2 = -x. This equation represents a sideways parabola that opens to the left. The vertex of this parabola is at the origin (0, 0), and the parabola extends to the left along the negative x-axis.

Conclusion

The equation у² = -х indeed represents a valid mathematical relationship, and it corresponds to a sideways parabola in the coordinate plane. However, the original equation x * y^2 = 0 represents a different scenario, where the graph consists of the x-axis and the y-axis.

If you have further questions or need additional clarification, feel free to ask!