What is the Difference Between Linear Equation and Quadratic Equation?
🆚 Go to Comparative Table 🆚The main differences between linear and quadratic equations are as follows:
- Shape of the graph: A linear equation produces a straight line when graphed, whereas a quadratic equation produces a parabola.
- Slope: The slope of a quadratic polynomial is constantly changing, unlike the slope of a linear polynomial.
- Function behavior: A linear function is one-to-one, meaning that each value of x produces one and only one value of y. A quadratic function, however, is not one-to-one, as there may be two or more values of y for a single value of x.
- Equation form: A linear equation has the general form $$y = mx + d$$, where m and d are constants. A quadratic equation has the general form $$ax^2 + bx + c = 0$$, where a, b, and c are constants.
- Solving and graphing: Graphing a linear function is straightforward, as it involves plotting two points and drawing a line through them. Solving and graphing quadratic equations is more complex, as it requires additional steps.
On this pageWhat is the Difference Between Linear Equation and Quadratic Equation? Comparative Table: Linear Equation vs Quadratic Equation
Comparative Table: Linear Equation vs Quadratic Equation
Here is a table that highlights the differences between linear equations and quadratic equations:
Feature | Linear Equations | Quadratic Equations |
---|---|---|
Definition | A linear equation is a polynomial equation of the form $$y = mx + b$$, where $$m$$ and $$b$$ are constants. | A quadratic equation is a polynomial equation of the form $$y = ax^2 + bx + c$$, where $$a$$, $$b$$, and $$c$$ are constants. |
Graphical Representation | A linear equation produces a straight line when graphed. | A quadratic equation produces a parabola when graphed. |
Slope | The slope of a linear function is constant, represented by the coefficient $$m$$ in the linear equation. | The equation of a quadratic function can be rewritten in the form $$y = bx + a{x^2}$$, which shows that the coefficient $$a$$ determines the shape and orientation of the parabola. |
Common Applications | Linear equations are commonly used to model relationships between two variables that change at a constant rate, such as distance and time. | Quadratic equations are often used to model relationships between two variables that change at a quadratic rate, such as velocity and position in projectile motion problems. |
Remember that both linear and quadratic equations are types of polynomial equations, but they have distinct characteristics that set them apart.
Read more:
- Linear Equation vs Nonlinear Equation
- Linear vs Nonlinear Differential Equations
- Difference Equation vs Differential Equation
- Linear vs Logistic Regression
- Algebraic Expressions vs Equations
- Parallelogram vs Quadrilateral
- Algebra vs Calculus
- Angular Velocity vs Linear Velocity
- Linear Motion vs Non Linear motion
- Parabola vs Hyperbola
- Expression vs Equation
- Hyperbola vs Ellipse
- Algebra vs Trigonometry
- Line vs Line Segment
- Linear vs Quadratic Stark Effect
- Circle vs Ellipse
- Polynomial vs Monomial
- Hyperbola vs Rectangular Hyperbola
- Linear Momentum vs Angular Momentum