Math Problem Statement

Gambarlah grafik y=4x-x²

Solution

numpy as np import matplotlib.pyplot as plt

Define the function y = 4x - x^2

x = np.linspace(-2, 5, 400) y = 4*x - x**2

Create the plot

plt.figure(figsize=(6, 6)) plt.plot(x, y, label=r'$y=4x - x^2$', color='b') plt.title("Grafik y = 4x - x²") plt.xlabel("x") plt.ylabel("y") plt.axhline(0, color='black',linewidth=0.5) plt.axvline(0, color='black',linewidth=0.5) plt.grid(True) plt.legend() plt.show()Here is the graph of the equation y=4xx2y = 4x - x^2. It represents a downward-opening parabola, where the vertex is at the point (2,4)(2, 4), and the parabola intercepts the x-axis at x=0x = 0 and x=4x = 4.

Would you like to know more about how the graph is derived, or any specific details on its properties?

Related Questions:

  1. How do we find the vertex of the parabola y=4xx2y = 4x - x^2?
  2. What is the significance of the roots of the quadratic equation 4xx2=04x - x^2 = 0?
  3. How do we calculate the axis of symmetry for the given parabola?
  4. What happens if the equation is modified to y=4x+x2y = -4x + x^2?
  5. How do we apply the quadratic formula to solve for the x-intercepts?

Tip: The vertex of a quadratic function y=ax2+bx+cy = ax^2 + bx + c can be found using the formula x=b2ax = -\frac{b}{2a}. For y=4xx2y = 4x - x^2, this gives x=2x = 2, which is the x-coordinate of the vertex.

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Math Problem Analysis

Mathematical Concepts

Algebra
Quadratic Functions
Graphing Parabolas

Formulas

y = 4x - x^2
Vertex formula x = -b/2a

Theorems

Parabola Vertex Theorem
Roots of Quadratic Equations

Suitable Grade Level

Grades 8-10