Question

Y= 2х^2-4x постройте график по точкам помогииите пожалуйста

Answer 1

F(x)=2x^2-4x
2x^2-4x=0
2x(x-2)=0
2x=0 => x=0 
или
x-2=0 => x=2
x₁=0
x₂=2
     Таблица и график во вложении

Answer 2

Plotting a Quadratic Function

To plot the graph of the quadratic function Y = 2x^2 - 4x, we can start by finding some key points on the graph. These points will help us visualize the shape of the parabola represented by the function.

Key Points on the Graph

1. Vertex: The x-coordinate of the vertex of a quadratic function can be found using the formula x = -b/2a. In this case, the coefficient of x^2 (a) is 2, and the coefficient of x (b) is -4. Plugging these values into the formula gives us x = -(-4)/(2*2) = 1. To find the corresponding y-coordinate, we can substitute x = 1 into the function: Y = 2*1^2 - 4*1 = -2. Therefore, the vertex is at the point (1, -2). 2. x-intercepts: To find the x-intercepts, we can set Y = 0 and solve for x. This gives us the equation 0 = 2x^2 - 4x. Factoring out the common term, we get 0 = 2x(x - 2). So, the x-intercepts are at x = 0 and x = 2.

Plotting the Graph

Now that we have the vertex and the x-intercepts, we can plot these points on a graph and sketch the parabola.

Let's plot the points: - Vertex: (1, -2) - x-intercepts: (0, 0) and (2, 0)

We can see that the parabola opens upwards because the coefficient of x^2 is positive. The vertex is the lowest point on the graph.

import matplotlib.pyplot as plt
import numpy as np

# Define the function
def quadratic_function(x):
    return 2*x**2 - 4*x

# Generate x values
x = np.linspace(-1, 3, 100)  # Range of x values to plot

# Plot the function
plt.plot(x, quadratic_function(x), label='Y = 2x^2 - 4x')
plt.scatter([0, 1, 2], [0, -2, 0], color='red')  # Plot the key points
plt.annotate('(0, 0)', xy=(0, 0), xytext=(-0.5, 0.5), textcoords='offset points')
plt.annotate('(1, -2)', xy=(1, -2), xytext=(1, -20), textcoords='offset points')
plt.annotate('(2, 0)', xy=(2, 0), xytext=(2, 10), textcoords='offset points')

# Add labels and title
plt.xlabel('x')
plt.ylabel('Y')
plt.title('Graph of Y = 2x^2 - 4x')
plt.axhline(0, color='black',linewidth=0.5)
plt.axvline(0, color='black',linewidth=0.5)
plt.grid(color = 'gray', linestyle = '--', linewidth = 0.5)
plt.legend()

# Show the plot
plt.show()

The graph of the function Y = 2x^2 - 4x is a parabola that opens upwards, with the vertex at (1, -2) and x-intercepts at (0, 0) and (2, 0).