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# Try our Free Online Math Solver! Online Math Solver

 Depdendent Variable

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 Dependent Variable

 Number of inequalities to solve: 23456789
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Definition: A quadratic function is a function which can be put in the form (General Form) or (Standard or Vertex Form )

For a quadratic functions or : 0) The domain of a quadratic function is 1) Graph : a (vertical) parabola

2) Opens up if 3) Opens down if 4) Vertex: with and 5) The x- intercept (s) can be found by setting and solving for x .

6) The y- intercept an be found by setting and solving for y .

Remark: The above items can be used to sketch the graph of a quadratic function

Examples:

Remark: The conversion from vertex form to general from is very easy. For conversion from general form to vertex form
we use the method of Completing Square .

Example:

The Maximum and the Minimum of a Quadratic Function (Parabola):

As was discussed above, the vertex of a parabola is with and a) If the parabola opens up, the vertex will be the lowest point and we say that the parabola has the minimum value
of at .

b) If the parabola opes down, the vertex will be the highest point and we say that the parabola has the maximum
value of at .

Remark: The coordinates of the vertex can be found by a graphing calculator .

Examples:

Application:

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