[1] For example, for the family of quadratic functions having the general form the simplest function is and every quadratic may be converted to that form by translations and dilations, which may be seen by completing the square.
This is therefore the parent function of the family of quadratic equations.
For example, the graph of y = A sin(x) + B cos(x) can be obtained from the graph of y = sin(x) by translating it through an angle α along the positive X axis (where tan(α) = A⁄B), then stretching it parallel to the Y axis using a stretch factor R, where R2 = A2 + B2.
Alternatively, the parent function may be interpreted as cos(x).
The concept of parent function is less clear or inapplicable polynomials of higher degree because of the extra turning points, but for the family of n-degree polynomial functions for any given n, the parent function is sometimes taken as xn, or, to simplify further, x2 when n is even and x3 for odd n. Turning points may be established by differentiation to provide more detail of the graph.