Transformation of Quadratic Functions Practice

Front

What is a horizontal translation of a function?

Back

A horizontal translation shifts the graph of a function left or right without changing its shape.

Front

How does the function g(x) = (x + 4)² relate to f(x) = x²?

Back

It represents a horizontal translation of f(x) 4 units to the left.

Front

What is a vertical translation of a function?

Back

A vertical translation shifts the graph of a function up or down without changing its shape.

Front

If g(x) = x² - 5, how does it transform from f(x) = x²?

Back

It represents a vertical translation down 5 units.

Front

What does the coefficient in front of (x - h)² in the vertex form of a quadratic function indicate?

Back

It indicates a vertical stretch or compression of the graph.

Front

What transformation occurs in the function f(x) = 5(x + 3)² - 10?

Back

It includes a vertical stretch by a factor of 5, a horizontal translation left 3 units, and a vertical translation down 10 units.

Front

What does a negative coefficient in front of x² indicate?

Back

It indicates a reflection of the graph across the x-axis.

Front

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

Back

If the coefficient of (x - h)² is greater than 1, the graph is vertically stretched.

Front

What is the effect of a horizontal compression on a quadratic function?

Back

It makes the graph narrower, occurring when the coefficient of (x - h)² is between 0 and 1.

Front

What transformation is represented by g(x) = -3x²?

Back

It represents a reflection across the x-axis and a vertical stretch by a factor of 3.