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) = ax² + bx + c, where a, b, and c are constants.

Front

What does the vertex of a quadratic function represent?

Back

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

Front

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

Back

The value of 'a' determines the direction of the opening (upward if a > 0, downward if a < 0) and the vertical stretch or compression of the graph.

Front

What is the effect of shifting a quadratic function vertically?

Back

Shifting a quadratic function vertically involves adding or subtracting a constant from the function, which moves the graph up or down without changing its shape.

Front

What is the effect of shifting a quadratic function horizontally?

Back

Shifting a quadratic function horizontally involves adding or subtracting a constant inside the parentheses, which moves the graph left or right.

Front

What does it mean for a quadratic function to be vertically stretched?

Back

A quadratic function is vertically stretched when the absolute value of 'a' is greater than 1, making the graph narrower.

Front

What does it mean for a quadratic function to be vertically compressed?

Back

A quadratic function is vertically compressed when the absolute value of 'a' is between 0 and 1, making the graph wider.

Front

How can you identify the direction a quadratic graph opens?

Back

The direction a quadratic graph opens can be identified by the sign of 'a': if a > 0, it opens upwards; if a < 0, it opens downwards.

Front

What is the standard form of a quadratic function?

Back

The standard form of a quadratic function is f(x) = ax² + bx + c.

Front

What is the vertex form of a quadratic function?

Back

The vertex form of a quadratic function is f(x) = a(x - h)² + k, where (h, k) is the vertex.