Science, Tech, Math › Math Quadratic Function - Parent Function and Vertical Shifts Share Flipboard Email Print BFG Images/Getty Images Math Pre Algebra & Algebra Math Tutorials Geometry Arithmetic Statistics Exponential Decay Functions Worksheets By Grade Resources View More By Jennifer Ledwith Math Expert B.B.A., Finance and Economics, University of Oklahoma Jennifer Ledwith is the owner of tutoring and test-preparation company Scholar Ready, LLC and a professional writer, covering math-related topics. our editorial process Jennifer Ledwith Updated November 05, 2019 A parent function is a template of domain and range that extends to other members of a function family. 01 of 06 Common Traits of Quadratic Functions 1 vertex1 line of symmetryThe highest degree (the greatest exponent) of the function is 2The 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 - 5y = x2 - 3x + 13y = -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. 02 of 06 Vertical Translations: Upward and Downward You can also look at a quadratic function in this light: y = x2 + c, x ≠ 0 When you start with the parent function, c = 0. Therefore, the vertex (the highest or lowest point of the function) is located at (0,0). Quick Translation Rules Add c, and the graph will shift up from the parent c units.Subtract c, and the graph will shift down from the parent c units. 03 of 06 Example 1: Increase c When 1 is added to the parent function, the graph sits 1 unit above the parent function. The vertex of y = x2 + 1 is (0,1). 04 of 06 Example 2: Decrease c When 1 is subtracted from the parent function, the graph sits 1 unit below the parent function. The vertex of y = x2 - 1 is (0,-1). 05 of 06 Example 3: Make a Prediction How does y = x2 + 5 differ from the parent function, y = x2? 06 of 06 Example 3: Answer The function, y = x2 + 5 shifts 5 units upward from the parent function. Notice that the vertex of y = x2 + 5 is (0,5), while the vertex of the parent function is (0,0).