Quadratic Function

Definition of Quadratic Function

  • Quadratic function is a function that can be described by an equation of the form
  • 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 , where

a  0 is called a quadratic equation.

  • Quadratic formula: A quadratic formula is the solution of a quadratic equation  given by .
  • Quadratic inequality: An inequality written in one of the forms , , , or  is called a quadratic inequality.
  • Quadratic term: A term  is the quadratic term in the equation
 

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

                                                  

Additional Links for Quadratic Function