The parent function of a quadratic equation is the simplest form of a quadratic function. It is represented as:
f(x) = x2
This function is called the parent function because it is the most basic quadratic function, and all other quadratic functions can be derived from it through transformations such as shifting, stretching, or reflecting.
In the parent function, the graph is a parabola that opens upwards, with its vertex at the origin (0, 0). The axis of symmetry is the y-axis, and the parabola is symmetric about this line.
Understanding the parent function is crucial because it helps in analyzing and graphing more complex quadratic functions. By knowing how the parent function behaves, you can predict how changes to the equation will affect the graph.