Transformations of Quadratic Functions

Front

What is the parent function of a quadratic equation?

Back

The parent function of a quadratic equation is f(x) = x², which is a parabola that opens upwards with its vertex at the origin (0,0).

Front

What does a vertical shift of a quadratic function do?

Back

A vertical shift moves the graph of the function up or down. For example, f(x) = x² + 3 shifts the graph up 3 units.

Front

What does a horizontal shift of a quadratic function do?

Back

A horizontal shift moves the graph of the function left or right. For example, f(x) = (x - 4)² shifts the graph right 4 units.

Front

What effect does a negative sign in front of a quadratic function have?

Back

A negative sign reflects the graph across the x-axis. For example, g(x) = -x² is a downward-opening parabola.

Front

What is a vertical stretch in the context of quadratic functions?

Back

A vertical stretch occurs when the coefficient of x² is greater than 1, making the parabola narrower. For example, f(x) = 3x² is vertically stretched by a factor of 3.

Front

What is a vertical compression in the context of quadratic functions?

Back

A vertical compression occurs when the coefficient of x² is between 0 and 1, making the parabola wider. For example, f(x) = 1/2x² is vertically compressed by a factor of 1/2.

Front

How do you identify a horizontal shift in the equation y = (x + 2)²?

Back

The equation y = (x + 2)² indicates a horizontal shift left by 2 units from the parent function.

Front

What does the equation g(x) = (x - 5)² represent in terms of transformations?

Back

The equation g(x) = (x - 5)² represents a horizontal shift right by 5 units from the parent function.

Front

What is the effect of adding a constant outside the quadratic function?

Back

Adding a constant outside the function, like in f(x) = x² + 4, results in a vertical shift up by that constant.

Front

What does the term 'reflection' mean in transformations of quadratic functions?

Back

Reflection means flipping the graph over a specific axis. For example, g(x) = -x² reflects the graph over the x-axis.