Transformations of Quadratic Functions

Front

What is a transformation of a quadratic function?

Back

A transformation of a quadratic function is a change made to the function that alters its graph, such as shifting, stretching, or reflecting.

Front

What does the equation g(x) = 2f(x) represent?

Back

It represents a vertical stretch of the function f(x) by a factor of 2.

Front

What does the equation g(x) = f(x + 2) represent?

Back

It represents a horizontal shift of the function f(x) 2 units to the left.

Front

What does the equation g(x) = f(x) - 3 represent?

Back

It represents a vertical shift of the function f(x) down by 3 units.

Front

What happens to the graph of f(x) = x² when it is transformed to g(x) = (x + 4)²?

Back

The graph shifts 4 units to the left.

Front

What does a vertical stretch do to the graph of a quadratic function?

Back

It makes the graph narrower.

Front

What does a vertical compression do to the graph of a quadratic function?

Back

It makes the graph wider.

Front

What is the effect of replacing f(x) with 3f(x)?

Back

It represents a vertical stretch by a factor of 3.

Front

What does the equation g(x) = x² - 5 represent?

Back

It represents a vertical shift of the function f(x) down by 5 units.

Front

What does the equation g(x) = (x - 5)² represent?

Back

It represents a horizontal shift of the function f(x) 5 units to the right.