Quadratic Transformations

Front

What is the vertex form of a quadratic function?

Back

The vertex form of a quadratic function is f(x) = a(x-h)² + k, where (h,k) is the vertex.

Front

Identify the vertex of the function f(x) = -2(x+1)² + 3.

Back

The vertex is (-1, 3).

Front

What does it mean to reflect a graph over the x-axis?

Back

Reflecting a graph over the x-axis means that for every point (x, y) on the graph, the point (x, -y) will also be on the graph.

Front

How does the graph of f(x) = x² compare to f(x) = -x²?

Back

The graph of f(x) = -x² is a reflection of f(x) = x² over the x-axis.

Front

What effect does the coefficient 'a' have in the vertex form f(x) = a(x-h)² + k?

Back

The coefficient 'a' determines the direction of the parabola (upward if a > 0, downward if a < 0) and its width (narrower if |a| > 1, wider if |a| < 1).

Front

What does it mean to shift a graph 4 units to the left?

Back

To shift a graph 4 units to the left, you replace x with (x + 4) in the function.

Front

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

Back

Adding a constant to a quadratic function shifts the graph vertically. For example, f(x) = x² + 2 shifts the graph up by 2 units.

Front

How do you determine the axis of symmetry for a quadratic function in vertex form?

Back

The axis of symmetry is the vertical line x = h, where (h,k) is the vertex of the function.

Front

What is the relationship between the graphs of f(x) = x² + 9 and g(x) = x² - 11?

Back

The graph of f(x) is 20 units above the graph of g(x).

Front

What does it mean to compress a graph vertically by a factor of 1/2?

Back

Compressing a graph vertically by a factor of 1/2 means that the y-values of the function are halved, making the graph narrower.