Parent Functions

Front

What is a parent function?

Back

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|).

Front

What is the parent function of a quadratic function?

Back

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).

Front

What is the parent function of an absolute value function?

Back

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).

Front

What is the parent function of a linear function?

Back

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.

Front

What is the parent function of a cubic function?

Back

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

Front

What is the general form of a quadratic function?

Back

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

Front

How does the graph of f(x) = x² change when a > 1?

Back

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

Front

How does the graph of f(x) = x² change when a < 1?

Back

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

Front

What effect does a negative 'a' have in the function f(x) = ax²?

Back

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

Front

What is the vertex form of a quadratic function?

Back

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