Quadratic Transformations, A.7C

Front

What is a vertical stretch in quadratic transformations?

Back

A vertical stretch occurs when the coefficient of the quadratic term (a) is greater than 1, making the graph narrower.

Front

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

Back

Reflecting a graph across 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 a horizontal translation affect the graph of a quadratic function?

Back

A horizontal translation shifts the graph left or right without changing its shape. For example, f(x) = (x - h)² shifts the graph h units to the right.

Front

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

Back

A negative coefficient reflects the graph across the x-axis, changing the direction of the parabola.

Front

What transformation occurs when the function f(x) = x² is changed to f(x) = x² + k?

Back

This transformation is a vertical translation, shifting the graph up by k units if k is positive and down if k is negative.

Front

What does it mean to compress a graph vertically?

Back

A vertical compression occurs when the coefficient of the quadratic term (a) is between 0 and 1, making the graph wider.

Front

How do you identify a reflection across the y-axis in a quadratic function?

Back

A reflection across the y-axis occurs when the function is transformed from f(x) to f(-x), flipping the graph horizontally.

Front

What is the transformation from y = x² to y = (x + 3)²?

Back

This transformation is a horizontal translation 3 units to the left.

Front

What does the vertex of a parabola represent?

Back

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

Front

How does the value of 'a' in y = a(x - h)² + k affect the graph?

Back

The value of 'a' affects the width and direction of the parabola: if |a| > 1, it stretches; if 0 < |a| < 1, it compresses; if a < 0, it reflects.