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 = x2, where x ≠ 0.
Here are a few quadratic functions:
- y = x2 - 5
- y = x2 - 3x + 13
- y = -x2 + 5x + 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.