系数

理解代数表达式中的系数

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 Type

x^2 coefficient: 2.0

x coefficient: -3.0

Constant: 1.0

x Value: 1.0

Show Graph

Expression Breakdown

2x^2 -3x + 1

Terms and Coefficients:

x^2 term

Coefficient: 2

x term

Coefficient: -3

Constant

Coefficient: 1

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

Function Curve

Current Point (x = 1.0)

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!

课程

个人学习单元

课程即将推出