Quadratic Transformations

Front

What is a quadratic function?

Back

A quadratic function is a polynomial function of degree 2, typically in the form f(x) = ax^2 + bx + c, where a, b, and c are constants and a ≠ 0.

Front

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

Back

Reflecting a quadratic function over the x-axis means multiplying the entire function by -1, which flips the graph upside down.

Front

What is a vertical stretch in the context of quadratic functions?

Back

A vertical stretch occurs when the coefficient 'a' in the quadratic function f(x) = ax^2 is greater than 1, making the graph narrower.

Front

What is a vertical compression in the context of quadratic functions?

Back

A vertical compression occurs when the coefficient 'a' in the quadratic function f(x) = ax^2 is between 0 and 1, making the graph wider.

Front

How does translating a quadratic function to the right affect its equation?

Back

Translating a quadratic function to the right by 'h' units changes the equation from f(x) = ax^2 to f(x) = a(x - h)^2.

Front

What is the vertex of a quadratic function?

Back

The vertex of a quadratic function is the highest or lowest point on the graph, depending on whether it opens upwards or downwards.

Front

How do you find the vertex of the function f(x) = a(x - h)^2 + k?

Back

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

Front

What does the 'h' value represent in the vertex form of a quadratic function?

Back

In the vertex form f(x) = a(x - h)^2 + k, 'h' represents the horizontal shift of the graph.

Front

What does the 'k' value represent in the vertex form of a quadratic function?

Back

In the vertex form f(x) = a(x - h)^2 + k, 'k' represents the vertical shift of the graph.

Front

What is the effect of a negative 'a' value in a quadratic function?

Back

A negative 'a' value in a quadratic function indicates that the graph opens downwards.