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.

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, y = ax2 + bx + c, y = ax2 + 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

Video Examples: Quadratic Functions


Examples of Quadratic Function

    The following are few examples of quadratic functions.

Solved Example on Quadratic Function

Ques: Graph the quadratic function y = - (1/4)x2.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.