Science, Tech, Math › Math Parabola Changes in Quadratic Functions Share Flipboard Email Print 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 August 07, 2019 You can use quadratic functions to explore how the equation affects the shape of a parabola. Here's how to make a parabola wider or narrower or how to rotate it onto its side. 01 of 06 Parent Function Mark Perry / Getty Images 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 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. Learn why a parabola opens wider, opens more narrow, or rotates 180 degrees. 02 of 06 Change a, Change the Graph Another form of the quadratic function is y = ax2 + c, where a≠ 0 In the parent function, y = x2, a = 1 (because the coefficient of x is 1). When the a is no longer 1, the parabola will open wider, open more narrow, or flip 180 degrees. Examples of Quadratic Functions where a ≠ 1: y = -1x2; (a = -1) y = 1/2x2 (a = 1/2)y = 4x2 (a = 4)y = .25x2 + 1 (a = .25) Change a, Change the Graph When a is negative, the parabola flips 180°.When |a| is less than 1, the parabola opens wider.When |a| is greater than 1, the parabola opens more narrow. Keep these changes in mind when comparing the following examples to the parent function. 03 of 06 Example 1: The Parabola Flips Compare y = -x2 to y = x2. Because the coefficient of -x2 is -1, then a = -1. When a is negative 1 or negative anything, the parabola will flip 180 degrees. 04 of 06 Example 2: The Parabola Opens Wider Compare y = (1/2)x2 to y = x2. y = (1/2)x2; (a = 1/2)y = x2; (a = 1) Because the absolute value of 1/2, or |1/2|, is less than 1, the graph will open wider than the graph of the parent function. 05 of 06 Example 3: The Parabola Opens More Narrow Compare y = 4x2 to y = x2. y = 4x2 (a = 4)y = x2; (a = 1) Because the absolute value of 4, or |4|, is greater than 1, the graph will open more narrow than the graph of the parent function. 06 of 06 Example 4: A Combination of Changes Compare y = -.25x2 to y = x2. y = -.25x2 (a = -.25)y = x2; (a = 1) Because the absolute value of -.25, or |-.25|, is less than 1, the graph will open wider than the graph of the parent function.