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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
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
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 .
The Maximum and the Minimum of a Quadratic Function (Parabola):
As was discussed above, the vertex of a parabola is with
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 .