Quadratic Transformations

Front

What is the vertex form of a quadratic function?

Back

f(x) = a(x-h)² + k

Front

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

Back

The y-values of the function are multiplied by -1, flipping the graph over the x-axis.

Front

How does a vertical compression affect the graph of a quadratic function?

Back

The graph becomes wider, as the y-values are multiplied by a factor between 0 and 1.

Front

What is the effect of shifting a graph 4 units to the right?

Back

The x-values of the function are decreased by 4.

Front

What does it mean to stretch a graph vertically by a factor of 2?

Back

The y-values of the function are multiplied by 2, making the graph narrower.

Front

How do you identify the vertex of a quadratic function in vertex form?

Back

The vertex is at the point (h, k) in the function f(x) = a(x-h)² + k.

Front

What transformation is represented by the equation y = -1/2(x-4)² + 1?

Back

Reflected across the x-axis, compressed by 1/2, shifted 4 units right and 1 unit up.

Front

What does it mean to shift a graph down 3 units?

Back

The y-values of the function are decreased by 3.

Front

How do you determine the direction of a parabola from its equation?

Back

If the coefficient of x² is positive, it opens upwards; if negative, it opens downwards.

Front

What is the effect of shifting a graph 4 units up?

Back

The y-values of the function are increased by 4.