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

Examples of Quadratic Function

The following are few examples of quadratic functions.

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


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.

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