parent functions and transformations

Front

What is a parent function?

Back

A parent function is the simplest form of a function in a family of functions, which retains the essential characteristics of that family.

Front

What does it mean to translate a graph left or right?

Back

Translating a graph left or right involves shifting the entire graph horizontally. A positive value shifts it left, while a negative value shifts it right.

Front

What is the effect of reflecting a graph across the x-axis?

Back

Reflecting a graph across the x-axis inverts the y-values of the function, resulting in a mirror image of the graph over the x-axis.

Front

What is the effect of reflecting a graph across the y-axis?

Back

Reflecting a graph across the y-axis inverts the x-values of the function, resulting in a mirror image of the graph over the y-axis.

Front

How do you represent a vertical shift of a function?

Back

A vertical shift is represented by adding or subtracting a constant from the function. For example, f(x) + k shifts the graph up k units, while f(x) - k shifts it down k units.

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 do you shift a quadratic function to the right?

Back

To shift a quadratic function to the right by h units, replace x with (x - h) in the function. For example, f(x) = (x - h)².

Front

What is the effect of a negative coefficient in front of a quadratic function?

Back

A negative coefficient in front of a quadratic function reflects the graph across the x-axis, making it open downwards.

Front

What does the vertex of a parabola represent?

Back

The vertex of a parabola represents the highest or lowest point of the graph, depending on whether it opens upwards or downwards.

Front

How do you identify the vertex of the function f(x) = a(x - h)² + k?

Back

The vertex of the function f(x) = a(x - h)² + k is the point (h, k).