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Difference Between Linear Function and Quadratic Functions

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Basic difference between linear function and quadratic functions is that linear function is the function, in which the value of the dependent variable depends only on the first power of the independent variable. But, in the quadratic function, value of the dependent variables depends on the second power of the independent variable.

Let’s see the basic difference between linear and quadratic equation.

Consider $y = ax + b$.
This is a simple linear function. In this function, $y$ is the dependent variable and $x$ is the independent variable.

In this, $y$ depends on $x^1$. $a$ and $b$ are constants and $a$ is not equal to zero.

In linear function, the power of the independent variable should be one. This means the highest degree of the equation should be one.

Graph of a linear equation is a straight line.

Example:

Solve the linear equation $x + 1 = 3$.

Solution:

Step 1: Subtract 1 from both the sides.

$x + 1 - 1 = -3 - 1$

Step 2: Simplify both the sides.

$x = -4$

This is the example of a simple linear equation. In this equation, power of $x$ is one.

$x + y = 1$ is another example of linear equation. Graph of this equation will be a straight line.

So, we can say that the graph of a linear equation is always a straight line.

In the case of a quadratic function, the value of the dependent variables depends on second power of the independent variable.

General form of a quadratic equation is $y = ax^2 + bx + c$. In this equation, $a$, $b$, $c$ are constants and $y$ depends on $x^2$. In this equation, $a$ is not equal to zero.

Example:

Solve $(x + 1)(x - 3) = 0$

Solution:

$x + 1 = 0$ or $x - 3 = 0$

$x = -1$ or $x = 3$

Therefore, the solution is $x = -1, 3$.