Parent Functions

A parent function is the simplest form of a function type, which serves as a foundation for more complex functions. Examples include linear functions (f(x) = x), quadratic functions (f(x) = x²), and absolute value functions (f(x) = |x|).

The parent function of a quadratic function is f(x) = x². It is a parabola that opens upwards with its vertex at the origin (0,0).

The parent function of an absolute value function is f(x) = |x|. It forms a V-shape graph with its vertex at the origin (0,0).

The parent function of a linear function is f(x) = x. It represents a straight line that passes through the origin with a slope of 1.

The parent function of a cubic function is f(x) = x³. It has an S-shaped curve that passes through the origin.

The general form of a quadratic function is f(x) = ax² + bx + c, where a, b, and c are constants.

When a > 1, the graph of f(x) = ax² becomes narrower, indicating that it opens more steeply.

When 0 < a < 1, the graph of f(x) = ax² becomes wider, indicating that it opens more gently.

If 'a' is negative, the graph of f(x) = ax² opens downwards, creating a concave shape.

The vertex form of a quadratic function is f(x) = a(x - h)² + k, where (h, k) is the vertex of the parabola.