Quadratic Transformations

Front

What is a vertical stretch in a quadratic function?

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 shift a graph up by 4 units?

Back

Shifting a graph up by 4 units means adding 4 to the y-values of all points on the graph.

Front

What is a vertical compression in a quadratic function?

Back

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

Front

How does reflecting a graph over the x-axis affect its equation?

Back

Reflecting a graph over the x-axis changes the sign of the quadratic term, resulting in a negative coefficient.

Front

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

Back

Shifting a graph left by 4 units means subtracting 4 from the x-values of all points on the graph.

Front

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

Back

Shifting a graph right by 4 units means adding 4 to the x-values of all points on the graph.

Front

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

Back

In vertex form, y = a(x-h)² + k, the vertex is the point (h, k).

Front

What is the standard form of a quadratic function?

Back

The standard form of a quadratic function is y = ax² + bx + c.

Front

What is the significance of the 'a' value in a quadratic function?

Back

The 'a' value determines the direction of the parabola (upward if a > 0, downward if a < 0) and its width.

Front

How do you determine if a quadratic function opens upwards or downwards?

Back

If the coefficient 'a' is positive, the parabola opens upwards; if 'a' is negative, it opens downwards.