Question

Исследовать функцию и построить график у= 4х^2​

Answer 1

Функция бесконечно возрастающая с наименьшим значением в точке (0;0), Область определений; X ⊃ (-∞; +∞)

         Область значений; y ⊃ [0; +∞)

Answer 2

Function Analysis and Graph Plotting

To analyze the function y = 4x^2, let's examine its properties and plot its graph.

The function y = 4x^2 is a quadratic function, which means it is a polynomial of degree 2. The coefficient of the x^2 term is 4, and there is no x term or constant term.

To plot the graph of the function, we can start by selecting some x-values and calculating the corresponding y-values. Let's choose a range of x-values from -5 to 5 and calculate the corresponding y-values:

| x | y | |---|---| | -5 | 100 | | -4 | 64 | | -3 | 36 | | -2 | 16 | | -1 | 4 | | 0 | 0 | | 1 | 4 | | 2 | 16 | | 3 | 36 | | 4 | 64 | | 5 | 100 |

Now, let's plot these points on a graph:

import matplotlib.pyplot as plt

x = [-5, -4, -3, -2, -1, 0, 1, 2, 3, 4, 5]
y = [100, 64, 36, 16, 4, 0, 4, 16, 36, 64, 100]

plt.plot(x, y)
plt.xlabel('x')
plt.ylabel('y')
plt.title('Graph of y = 4x^2')
plt.grid(True)
plt.show()

The graph of the function y = 4x^2 is a parabola that opens upwards. It is symmetric with respect to the y-axis and passes through the origin (0, 0). The vertex of the parabola is at the point (0, 0), and the axis of symmetry is the y-axis.

Conclusion

In conclusion, the function y = 4x^2 is a quadratic function that represents a parabola opening upwards. Its graph is symmetric with respect to the y-axis and passes through the origin. The vertex of the parabola is at the point (0, 0), and the axis of symmetry is the y-axis.

Please let me know if there's anything else I can help you with!