Koeffizient
Verstehen von Koeffizienten in algebraischen Ausdrücken
Interactive Coefficient Visualization
Introduction
A coefficient is the numerical factor that multiplies a variable in an algebraic expression. Coefficients determine the shape, slope, and behavior of mathematical functions.
Key Concepts:
- Coefficient: The number multiplying a variable (e.g., in 3x, 3 is the coefficient)
- Leading Coefficient: The coefficient of the highest degree term
- Constant Term: A term with no variable (coefficient of x⁰)
- Impact: Changing coefficients changes the graph's shape, steepness, and position
- Sign: Positive coefficients create upward trends, negative create downward trends
How to Use
- Select an expression type to see different polynomial forms
- Use the coefficient sliders to adjust each coefficient and see how it affects the graph
- Hover over coefficient sliders to highlight the corresponding term
- Use the x-value slider to evaluate the expression at different points
- Observe how changing coefficients changes the shape, position, and behavior of the curve
- Try creating custom expressions to explore different coefficient combinations
Expression Breakdown
2x^2 -3x + 1
Terms and Coefficients:
Evaluation
Expression: 2x^2 -3x + 1
At x = 1.0: 2(1.0)^2 -3(1.0) + 1 = 0.0000
Graph: y = 2x^2 -3x + 1
How Coefficients Affect the Graph
Leading Coefficient:
Controls the overall direction and steepness. Positive values make the curve open upward, negative values open downward.
Linear Coefficient:
Affects the slope and horizontal position of the curve. Larger absolute values create steeper slopes.
Constant Term:
Shifts the entire graph vertically. Positive values move it up, negative values move it down.
Try It:
Adjust the coefficient sliders above and watch how the graph changes in real-time!
Lektionen
Einzelne Lerneinheiten
Lektionen kommen bald