Algebra 2 Transformations Flashcards

Questions and Answers

What is the equation for a Horizontal Translation?

y = f(x-h)

What is the equation for a Vertical Translation?

y = f(x) + k

What is the equation for a Reflection in the X-axis?

y = -f(x)

What is the equation for a Reflection in the Y-axis?

y = f(-x) Signup and view all the answers

What is the equation for Horizontal Stretches and Shrinks?

y = f(ax) by a factor of 1/a Signup and view all the answers

What is the equation for Vertical Stretches and Shrinks?

y = a * f(x) by a factor of a Signup and view all the answers

What is the standard form of a Quadratic Function?

f(x) = a(x-h)^2 + k Signup and view all the answers

What is the standard form of an Absolute Value Function?

f(x) = a|x-h| + k Signup and view all the answers

What are the coordinates of a Vertex?

(h, k) Signup and view all the answers

Study Notes

Translations in Algebra 2

Horizontal Translation: Adjusts the graph of a function left or right. Defined by the equation (y = f(x - h)), where (h) indicates the horizontal shift.
Vertical Translation: Shifts the graph up or down. This is represented by the equation (y = f(x) + k), where (k) changes the vertical position.
Reflection in the X-axis: This transformation flips the graph over the X-axis. The corresponding equation is (y = -f(x)), reversing the sign of the function's output.
Reflection in the Y-axis: Alters the graph by flipping it over the Y-axis. It is expressed as (y = f(-x)), effectively changing the input variable's sign.
Horizontal Stretches and Shrinks: Adjusts the width of the graph. The relationship is defined by (y = f(ax)), where (a) determines the level of stretch (if (0 < a < 1), it stretches and if (a > 1), it shrinks).
Vertical Stretches and Shrinks: Changes the height of the graph. This is captured in the equation (y = a * f(x)), where (a) influences the graph's vertical scaling; if (a > 1), it stretches, and if (0 < a < 1), it shrinks.
Quadratic Function: A specific type of polynomial function represented as (f(x) = a(x - h)^2 + k). It includes parameters (a) (affects width and direction), (h) (horizontal position), and (k) (vertical position).
Absolute Value Function: Defined as (f(x) = a|x - h| + k). This function produces a V-shaped graph and includes parameters for vertical and horizontal transformations.
Vertex: The point representing the highest or lowest point on the graph of a quadratic or absolute value function, depicted as ((h, k)). This point is critical for identifying the function's orientation and position.

Description

Test your understanding of various transformations in Algebra 2 with these flashcards. Each card includes a term related to function transformations along with its mathematical definition. Perfect for reinforcing key concepts in your Algebra 2 studies.