Question

Срочно нужна Ваша помощь! исследуйте функцию и постройте ее график y=x^2-5x

Answer 1

Ответ:

Объяснение:

Решение на фотке

Answer 2

Function Analysis and Graph Plotting

To analyze the function y = x^2 - 5x, let's first understand its key properties and then plot its graph.

1. Function Properties: - The given function is a quadratic function, which means it is a second-degree polynomial. - The general form of a quadratic function is y = ax^2 + bx + c, where a, b, and c are constants.

2. Analysis of the Given Function: - For the function y = x^2 - 5x, the coefficient of the x^2 term is 1, the coefficient of the x term is -5, and there is no constant term (c = 0). - The vertex of the parabola represented by this function can be found using the formula x = -b/(2a). In this case, a = 1 and b = -5.

3. Graph Plotting: - Let's plot the graph of the function y = x^2 - 5x to visualize its shape and behavior.

import matplotlib.pyplot as plt
import numpy as np

# Define the function
def f(x):
    return x**2 - 5*x

# Generate x values
x = np.linspace(-2, 7, 100)  # Choosing a range that captures the shape of the parabola

# Generate y values
y = f(x)

# Plot the graph
plt.figure(figsize=(8, 6))
plt.plot(x, y, label='$y = x^2 - 5x$')
plt.scatter(-b/(2*a), f(-b/(2*a)), color='red', label='Vertex')  # Plot the vertex
plt.axhline(0, color='black',linewidth=0.5)
plt.axvline(0, color='black',linewidth=0.5)
plt.xlabel('x')
plt.ylabel('y')
plt.title('Graph of $y = x^2 - 5x$')
plt.legend()
plt.grid(True)
plt.show()

Conclusion

The graph of the function y = x^2 - 5x is a parabola that opens upwards. The vertex of the parabola is located at the point where the x-coordinate is 2.5 and the y-coordinate is -6.25. This information provides a visual representation of the behavior of the function.