What is the Difference Between Linear Equation and Quadratic Equation?

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.

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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.

Guilherme Mazui is graduated in journalism from the Federal University of Minas Gerais (UFMG) and a master's degree in Communication from the University of São Paulo (USP). In addition, he has experience in advertising writing and has worked as a content editor in several companies.