Translations

Front

What is a translation in the context of graph transformations?

Back

A translation is a type of transformation that shifts a graph horizontally and/or vertically without changing its shape or orientation.

Front

How does the equation y = (x - 3)^3 - 2 transform the graph of y = x^3?

Back

The graph is translated right by 3 units and down by 2 units.

Front

What effect does the term (x + 2) have on the graph of a function?

Back

The term (x + 2) translates the graph left by 2 units.

Front

What is the general form of a quadratic function?

Back

The general form is y = a(x - h)^2 + k, where (h, k) is the vertex of the parabola.

Front

How does the equation y = (x - 5)^2 - 3 transform the graph of y = x^2?

Back

The graph is translated right by 5 units and down by 3 units.

Front

What does the term -4 indicate in the function f(x) = √(x + 2) - 4?

Back

The term -4 indicates a vertical translation down by 4 units.

Front

What is the effect of the absolute value in the function f(x) = |x + 2| - 3?

Back

The absolute value creates a V-shaped graph, and the -3 translates it down by 3 units.

Front

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

Back

The vertex is given by the point (h, k) in the equation y = a(x - h)^2 + k.

Front

What transformation does the equation f(x) = (x - 2)^2 - 2 represent?

Back

The graph is translated right by 2 units and down by 2 units.

Front

What is the significance of the coefficient 'a' in the quadratic function y = a(x - h)^2 + k?

Back

The coefficient 'a' determines the direction and width of the parabola; if 'a' is positive, it opens upwards, and if negative, it opens downwards.