Question

Постройте график функции y=x*x-2x укажите при каких значениях x функция принимает отрицательные значения

Answer 1

Вот)))
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Answer 2

Plot of the Function y = x^2 - 2x

To plot the function y = x^2 - 2x, we can use a graphing tool or manually calculate the values of y for different values of x. Let's plot the graph:

import matplotlib.pyplot as plt
import numpy as np

x = np.linspace(-10, 10, 100)
y = x**2 - 2*x

plt.plot(x, y)
plt.xlabel('x')
plt.ylabel('y')
plt.title('Graph of y = x^2 - 2x')
plt.grid(True)
plt.show()

The graph of the function y = x^2 - 2x is a parabola that opens upwards. The vertex of the parabola is at the point (1, -1). The function takes negative values for x values less than 1.

Values of x for which the function takes negative values

To find the values of x for which the function y = x^2 - 2x takes negative values, we need to solve the inequality y < 0. Let's solve it:

x^2 - 2x < 0
x(x - 2) < 0

To solve this inequality, we can use a sign chart or test intervals. Let's use the sign chart method:

| x | x - 2 | x(x - 2) | |-------|-----------|--------------| | x < 0 | - | + | | 0 < x < 2 | - | - | | x > 2 | + | + |

From the sign chart, we can see that the function y = x^2 - 2x is negative when x is between 0 and 2, exclusive. In interval notation, the values of x for which the function takes negative values are (0, 2).

Note: The above analysis is based on the assumption that the function y = x^2 - 2x is defined for all real numbers. If there are any restrictions on the domain of the function, please provide them for a more accurate analysis.

Conclusion

The function y = x^2 - 2x is a parabola that opens upwards. It takes negative values for x values between 0 and 2, exclusive.