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In mathematics, a parent function is the simplest function of a family of functions that preserves the definition of the entire family. For example, for the family of quadratic functions having the general form
the simplest function is
This is therefore the parent function of the family of quadratic equations.
For linear and quadratic functions, the graph of any function can be obtained from the graph of the parent function by simple translations and stretches parallel to the axes. For example, the graph of y = x − 4x + 7 can be obtained from the graph of y = x by translating +2 units along the X axis and +3 units along Y axis. This is because the equation can also be written as y − 3 = .
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