Transformations of Functions

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

How does the graph of a quadratic function change when translated up by 5 units?

Back

The equation of the quadratic function becomes y = ax² + bx + (c + 5), shifting the entire graph upwards by 5 units.

Front

What does the transformation f(x) - 6 represent?

Back

This transformation represents a vertical shift of the graph downwards by 6 units.

Front

What is the effect of a vertical shrink by 1/2 on the graph of a function?

Back

A vertical shrink by 1/2 compresses the graph towards the x-axis, making it less steep.

Front

What does the transformation f(x + 5) indicate about the graph?

Back

This transformation indicates a horizontal shift of the graph to the left by 5 units.

Front

How do you describe the transformation of a function that moves right by 7 units?

Back

The transformation can be represented as f(x - 7), indicating a horizontal shift to the right.

Front

What is the parent graph of a quadratic function?

Back

The parent graph of a quadratic function is the graph of y = x², which is a parabola opening upwards.

Front

What is the significance of the vertex in a quadratic function?

Back

The vertex is the highest or lowest point of the parabola, depending on the direction it opens, and it represents the minimum or maximum value of the function.

Front

What does it mean for a function to be translated left by 1 unit?

Back

Translating a function left by 1 unit means replacing x with (x + 1) in the function's equation.

Front

How does the transformation f(x) + 3 affect the graph?

Back

This transformation shifts the graph of the function upwards by 3 units.