**Definition of Quadratic Function **

- Quadratic function is a function that can be described by an equation of the form
*f*(*x*) =*a**x*^{2}+*bx*+*c,*where*a*≠ 0. - In a quadratic function, the greatest power of the variable is 2. The graph of a quadratic function is a parabola.

**Examples of Quadratic Function**

- The following are few examples of quadratic functions.

**More about Quadratic Function**

**Quadratic equation:**An equation in the standard form*a**x*^{2}+*bx*+*c*= 0, where*a*≠ 0 is called a quadratic equation.**Quadratic formula:**A quadratic formula is the solution of a quadratic equation*a**x*^{2}+*bx*+*c*= 0, where*a*≠ 0, given by .**Quadratic inequality:**An inequality written in one of the forms*y*<>*a**x*^{2}+*bx*+*c*,*y*≥*a**x*^{2}+*bx*+*c*,*y*≤*a**x*^{2}+*bx*+*c*, or*y*>*a**x*^{2}+*bx*+*c*is called a quadratic inequality.**Quadratic term:**A term*a**x*^{2}is the quadratic term in the equation*f*(*x*) =*a**x*^{2}+*bx*+*c*

**Solved Example on Quadratic Function**

Graph the quadratic function . Indicate whether the parabola opens up or down.

Choices:

A. Graph-A; opens down

B. Graph-B; opens down

Correct Answer: A

Solution:

Step 1:Make a table of ordered pairs for the given function.

Step 2:Plot these points on the coordinate plane and connect the points with a smooth curve.

Step 3:The graph looks like the one below:

Step 4:It can be observed from the graph that the parabola opens down.

Step 5:The equation of the axis of symmetry is:x= 0.

Step 6:The vertex is at (0, 0).

Step 7:The parabola opens down. So, the vertex is the maximum point.

**Related Terms for Quadratic Function**

- Equation
- Power
- Parabola
- Quadratic Equation
- Quadratic Formula
- Quadratic Inequality
- Quadratic Term