Parent Functions pdf

Parent Functions pdf

In mathematics, a parent function is the simplest function of a family of functions that preserves the definition (or shape) of the entire family. For example, for the family of quadratic functions having the general form : $y=ax^{2}+bx+c\,,$

the simplest function is : $y=x^{2}$ .

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 = x² − 4x + 7 can be obtained from the graph of y = x² 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 = (x − 2)².