quadratic function


Definition of Quadratic Function

  • Quadratic function is a function that can be described by an equation of the form f(x) = ax2 + 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 ax2 + bx + c = 0, where a ≠ 0 is called a quadratic equation.
  • Quadratic formula: A quadratic formula is the solution of a quadratic equation ax2 + bx + c = 0, where a ≠ 0, given by .
  • Quadratic inequality: An inequality written in one of the forms y <>ax2 + bx + c, yax2 + bx + c, yax2 + bx + c, or y > ax2 + bx + c is called a quadratic inequality.
  • Quadratic term: A term ax2 is the quadratic term in the equation f(x) = ax2 + 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