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 . It represents a downward-opening parabola, where the vertex is at the point , and the parabola intercepts the x-axis at and .
Would you like to know more about how the graph is derived, or any specific details on its properties?
Related Questions:
- How do we find the vertex of the parabola ?
- What is the significance of the roots of the quadratic equation ?
- How do we calculate the axis of symmetry for the given parabola?
- What happens if the equation is modified to ?
- How do we apply the quadratic formula to solve for the x-intercepts?
Tip: The vertex of a quadratic function can be found using the formula . For , this gives , 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