Transformations of Quadratic Functions 2023

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 functions?

Back

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

Front

What does it mean to reflect a quadratic function across the x-axis?

Back

Reflecting a quadratic function across the x-axis means that the output values (y-values) are multiplied by -1, resulting in a downward-opening parabola.

Front

What is a vertical compression in the context of quadratic functions?

Back

A vertical compression occurs when the coefficient 'a' in the function f(x) = ax² is between 0 and 1, making the parabola wider.

Front

What does a horizontal shift to the right mean for a quadratic function?

Back

A horizontal shift to the right means that the function is transformed to f(x) = (x - h)², where h is a positive number.

Front

What does a vertical shift up mean for a quadratic function?

Back

A vertical shift up means that a constant is added to the function, resulting in f(x) = x² + k, where k is a positive number.

Front

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

Back

The value of 'a' determines the direction of the parabola (upward if a > 0, downward if a < 0) and its width (narrower if |a| > 1, wider if 0 < |a| < 1).

Front

What is the effect of a negative 'a' in a quadratic function?

Back

A negative 'a' reflects the graph of the quadratic function across the x-axis.

Front

What does the term 'vertex' refer to in a quadratic function?

Back

The vertex is the highest or lowest point of the parabola, depending on whether it opens upward or downward.

Front

What is the significance of 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.