Transformations (Final Review)

Front

What is a transformation in mathematics?

Back

A transformation is an operation that moves or changes a shape in some way, such as translation, rotation, reflection, or dilation.

Front

What does it mean to translate a graph?

Back

To translate a graph means to shift it horizontally or vertically without changing its shape.

Front

How does the equation y = (x - 3)² transform the graph of y = x²?

Back

The graph is translated right 3 units.

Front

What is the effect of a negative sign in front of a quadratic function?

Back

It reflects the graph over the x-axis.

Front

What does the equation y = -x² + 2 represent?

Back

It is a quadratic function reflected over the x-axis and shifted up 2 units.

Front

Describe the transformations of the graph y = (x - 3)³ - 2.

Back

The graph is translated right 3 units and down 2 units.

Front

What does the equation y = x² + 5 indicate about the graph?

Back

The graph of y = x² is translated up 5 units.

Front

How do you identify a graph that has been shifted right 5 units?

Back

The equation will be in the form y = |x - 5|.

Front

What is the general form of a quadratic function?

Back

The general form is y = ax² + bx + c, where a, b, and c are constants.

Front

What is the vertex of a parabola?

Back

The vertex is the highest or lowest point of the parabola, depending on its orientation.