A **parent function** is a template of domain and range that extends to other members of a function family.

### Some Common Traits of Quadratic Functions

- 1 vertex
- 1 line of symmetry
- The highest degree (the greatest exponent) of the function is 2
- The graph is a parabola

### Parent and Offspring

The equation for the quadratic parent function is

y=x^{2}, wherex≠ 0.

Here are a few quadratic functions:

*y*=*x*^{2}- 5*y*=*x*^{2}- 3*x*+ 13*y*= -*x*^{2}+ 5*x*+ 3

The children are transformations of the parent. Some functions will shift upward or downward, open wider or more narrow, boldly rotate 180 degrees, or a combination of the above. This article focuses on vertical translations. Learn why a quadratic function shifts upward or downward.