Quadratic Transformations

Front

What is a quadratic transformation?

Back

A quadratic transformation refers to the changes made to the graph of a quadratic function, such as stretching, compressing, or shifting.

Front

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

Back

It means that for every point on the graph, the y-coordinate is multiplied by 2, making the graph narrower.

Front

What does it mean to compress a quadratic function vertically by a factor of 2?

Back

It means that for every point on the graph, the y-coordinate is divided by 2, making the graph wider.

Front

How does shifting a quadratic function to the left affect its equation?

Back

Shifting left involves replacing x with (x + h) in the equation, where h is the number of units shifted.

Front

How does shifting a quadratic function upward affect its equation?

Back

Shifting upward involves adding a constant to the entire function, increasing the y-values.

Front

What is the vertex form of a quadratic function?

Back

The vertex form is given by f(x) = a(x - h)² + k, where (h, k) is the vertex.

Front

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

Back

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

Front

What effect does a negative 'a' value have on the graph of a quadratic function?

Back

A negative 'a' value reflects the graph across the x-axis, making it open downwards.

Front

What is the significance of the 'k' value in the vertex form?

Back

The 'k' value represents the vertical shift of the graph; it indicates how far up or down the graph is moved.

Front

How do you determine the direction of opening for a quadratic function?

Back

The direction of opening is determined by the sign of 'a': if 'a' is positive, it opens upwards; if 'a' is negative, it opens downwards.

Tags

CCSS.HSF-IF.C.7A