Algebra 2: Parent Functions and Transformations

A parent function is the simplest form of a function type, which serves as a foundation for more complex functions. Examples include linear, quadratic, cubic, absolute value, and square root functions.

The equation of the absolute value parent function is y = |x|.

Shifting a graph to the right by 'h' units involves replacing 'x' with 'x - h' in the function's equation.

The equation of the square root parent function is y = √x.

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

To translate a quadratic function left by 'h' units, replace 'x' with 'x + h' in the function's equation.

The equation of the cubic parent function is y = x³.

A vertical stretch multiplies the output of the function by a factor greater than 1, making the graph steeper.

The equation of a transformed quadratic function that opens upwards is y = a(x - h)² + k, where 'a' > 0, (h, k) is the vertex.

Even functions are symmetric about the y-axis (f(x) = f(-x)), while odd functions are symmetric about the origin (f(-x) = -f(x)).