Quadratic Transformations

Front

What is a quadratic function?

Back

A quadratic function is a polynomial function of degree 2, typically written in the form y = ax² + bx + c, where a, b, and c are constants.

Front

What is the parent function of quadratic functions?

Back

The parent function of quadratic functions is y = x².

Front

What does a vertical shift in a quadratic function do?

Back

A vertical shift moves the graph of the function up or down without changing its shape.

Front

How does the equation y = x² + 5 transform the parent function?

Back

It shifts the graph of the parent function y = x² up by 5 units.

Front

What effect does a negative coefficient have on a quadratic function?

Back

A negative coefficient reflects the graph across the x-axis.

Front

What is a vertical stretch in a quadratic function?

Back

A vertical stretch occurs when the coefficient 'a' is greater than 1, making the graph narrower.

Front

What is a vertical shrink in a quadratic function?

Back

A vertical shrink occurs when the coefficient 'a' is between 0 and 1, making the graph wider.

Front

What transformation does the equation g(x) = (x + 4)² represent?

Back

It represents a horizontal shift of the graph 4 units to the left.

Front

How do you identify a vertical shift in a quadratic function?

Back

A vertical shift can be identified by the constant added or subtracted from the function, such as in y = x² + k.

Front

What does the transformation y = -3x² indicate?

Back

It indicates a reflection over the x-axis and a vertical stretch by a factor of 3.