Quadratic Transformations Review

Front

What is the parent function of a quadratic equation?

Back

The parent function of a quadratic equation is y = x².

Front

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

Back

This equation represents a translation 2 units to the right and 2 units down from the parent function.

Front

How does the equation y = (x + 3)² affect the graph of y = x²?

Back

This equation represents a translation 3 units to the left from the parent function.

Front

What does a negative sign in front of a quadratic function indicate?

Back

A negative sign indicates a reflection over the x-axis.

Front

What is the effect of multiplying a quadratic function by a fraction, such as y = (1/3)x²?

Back

Multiplying by a fraction compresses the graph vertically.

Front

What does the term 'translation' mean in the context of graph transformations?

Back

Translation refers to shifting the graph horizontally or vertically without changing its shape.

Front

What transformation is represented by the equation y = - (x - 7)² + 2?

Back

This equation represents a reflection over the x-axis, a translation 7 units to the right, and 2 units up.

Front

How do you identify a vertical stretch or compression in a quadratic function?

Back

A vertical stretch occurs when the coefficient of x² is greater than 1, while a compression occurs when it is between 0 and 1.

Front

What is the effect of adding a constant to a quadratic function, such as y = x² + 3?

Back

Adding a constant translates the graph vertically; in this case, it moves the graph up 3 units.

Front

What does the equation y = (x - 3)² represent in terms of transformations?

Back

This equation represents a translation 3 units to the right from the parent function.