Quadratic transformations

Front

What is a quadratic function?

Back

A quadratic function is a polynomial function of degree 2, typically in the form f(x) = ax² + bx + c, where a, b, and c are constants.

Front

What is the parent function of quadratic transformations?

Back

The parent function of quadratic transformations is f(x) = x².

Front

What does it mean to shift a graph up?

Back

Shifting a graph up means adding a positive constant to the function, resulting in a vertical translation.

Front

What does it mean to shift a graph down?

Back

Shifting a graph down means subtracting a positive constant from the function, resulting in a vertical translation.

Front

What is a reflection over the x-axis?

Back

A reflection over the x-axis occurs when the function is multiplied by -1, resulting in the graph being flipped vertically.

Front

What is a horizontal shift to the right?

Back

A horizontal shift to the right occurs when a positive constant is subtracted from the x variable in the function, resulting in a translation.

Front

What is a horizontal shift to the left?

Back

A horizontal shift to the left occurs when a positive constant is added to the x variable in the function, resulting in a translation.

Front

What does it mean for a quadratic function to be narrower?

Back

A quadratic function is narrower than the parent function if the coefficient 'a' is greater than 1, indicating a vertical stretch.

Front

What does it mean for a quadratic function to be wider?

Back

A quadratic function is wider than the parent function if the coefficient 'a' is between 0 and 1, indicating a vertical compression.

Front

How does the value of 'c' affect the graph of a quadratic function?

Back

The value of 'c' in the function f(x) = ax² + bx + c represents the y-intercept of the graph.