Transformations of parent functions

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 transformation occurs when a function is translated vertically?

Back

A vertical translation shifts the graph of the function up or down without changing its shape.

Tags

CCSS.HSF.BF.B.3

Front

How does the equation y = a(x - h)^2 + k represent a transformation of the parent function f(x) = x^2?

Back

In this equation, 'h' represents a horizontal shift, 'k' represents a vertical shift, and 'a' indicates a vertical stretch or compression and reflection.

Front

What does the 'a' value in the equation y = a|x| + b indicate?

Back

The 'a' value indicates the vertical stretch or compression of the absolute value function, and it can also reflect the graph across the x-axis if negative.

Front

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

Back

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

Front

How do you determine the vertex of a quadratic function in vertex form?

Back

The vertex of a quadratic function in vertex form y = a(x - h)^2 + k is the point (h, k).

Front

What does it mean to translate a function to the right by 'h' units?

Back

Translating a function to the right by 'h' units means replacing 'x' with 'x - h' in the function's equation.

Front

What is the general form of a quadratic function?

Back

The general form of a quadratic function is y = ax^2 + bx + c, where a, b, and c are constants.

Front

What transformation is represented by the equation y = x^2 + 5?

Back

The equation y = x^2 + 5 represents a vertical translation of the parent function y = x^2 up by 5 units.

Front

How does the transformation y = -|x| + 3 affect the graph of the absolute value function?

Back

The transformation y = -|x| + 3 reflects the graph of the absolute value function across the x-axis and translates it up by 3 units.