Writing Transformations of Functions

Front

What is the parent function of a quadratic equation?

Back

The parent function of a quadratic equation is f(x) = x².

Front

What does a vertical stretch of a function mean?

Back

A vertical stretch means that the function's values are multiplied by a factor greater than 1, making the graph narrower.

Front

How does the equation g(x) = 5x² + 2 transform the parent function f(x) = x²?

Back

It represents a vertical stretch by a factor of 5 and a vertical shift upward by 2 units.

Front

What is the effect of translating a function up by 5 units?

Back

The entire graph of the function moves up 5 units, which can be represented by adding 5 to the function's output.

Front

What does the transformation f(x + 5) represent?

Back

It represents a horizontal shift of the graph 5 units to the left.

Front

What is the effect of translating a function down by 3 units?

Back

The entire graph of the function moves down 3 units, which can be represented by subtracting 3 from the function's output.

Front

How do you identify a function that has been translated to the right?

Back

A function is translated to the right by replacing x with (x - h), where h is the number of units moved to the right.

Front

What does the transformation f(x - 7) indicate?

Back

It indicates a horizontal shift of the graph 7 units to the right.

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

What is the significance of the coefficient 'a' in a quadratic function?

Back

The coefficient 'a' determines the direction of the parabola (upward if a > 0, downward if a < 0) and the width of the parabola.