Parent Functions & Transformations

Front

What is a parent function?

Back

A parent function is the simplest form of a function type, which serves as a foundation for creating more complex functions through transformations.

Front

What is a quadratic function?

Back

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

Front

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

Back

Reflecting a function over the x-axis means to invert its output values, changing f(x) to -f(x).

Front

How does shifting a function vertically affect its graph?

Back

Shifting a function vertically involves adding or subtracting a constant from the function, which moves the graph up or down without changing its shape.

Front

What is the effect of the transformation f(x) + d?

Back

The transformation f(x) + d shifts the graph of the function vertically by d units; if d is positive, it shifts up, and if negative, it shifts down.

Front

What is the standard form of a quadratic function?

Back

The standard form of a quadratic function is y = ax² + bx + c, where a, b, and c are constants.

Front

What is the vertex of a quadratic function?

Back

The vertex of a quadratic function is the highest or lowest point on the graph, depending on the direction of the parabola.

Front

What does the term 'vertical translation' refer to?

Back

Vertical translation refers to moving the graph of a function up or down along the y-axis.

Front

What is the general form of a linear function?

Back

The general form of a linear function is y = mx + b, where m is the slope and b is the y-intercept.

Front

How do you identify a quadratic function from its graph?

Back

A quadratic function can be identified by its parabolic shape, which opens either upwards or downwards.