y = x2 is called the "parent function" of all quadratic functions. It is the most basic form of a quadratic function and can be transformed in infinitely many ways to create all other quadratic functions. We call it the "parent function" because we use it as a starting point from which to create other quadratic functions. Use the problems below to create graphs and visualize what transformations are being made to the parent function.
Graph x2 and x2 + 4 in desmos
What transformation occurred when x2 became x2 + 4?
Graph x2 and x2 - 6 in desmos
What transformation occurred when x2 became x2 - 6?
Graph x2 and (x - 1)2 in desmos
What transformation occurred when x2 became (x - 1)2?
Graph x2 and (x + 2)2 in desmos
What transformation occurred when x2 became (x + 2)2?
Match the function to its transformation from the parent function
| Draggable item | arrow_right_alt | Corresponding Item |
|---|---|---|
(x - 4)2 | arrow_right_alt | moved up 4 places |
(x + 5)2 | arrow_right_alt | moved down 4 places |
x2 - 5 | arrow_right_alt | moved right 4 places |
x2 + 5 | arrow_right_alt | moved left 4 places |
(x - 5)2 | arrow_right_alt | moved up 5 places |
x2 - 4 | arrow_right_alt | moved down 5 places |
(x + 4)2 | arrow_right_alt | moved left 5 places |
x2 + 4 | arrow_right_alt | moved right 5 places |
What would happen to the parent function if it became y = (x - 3)2 + 5?