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Quadratic Function - Parent Function and Vertical Shifts

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Quadratic Function - Parent Function and Vertical Shifts
Quadratic Parent Function

Quadratic Parent Function

Jennifer Ledwith

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.

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