Transformations of Quadratic Functions2024

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 of the parabola.

Front

What does the 'a' value in the quadratic function f(x) = a(x - h)² + k determine?

Back

The 'a' value determines the direction of the parabola (upward if a > 0, downward if a < 0) and its width (narrower if |a| > 1, wider if |a| < 1).

Front

How does a vertical shift affect the graph of a quadratic function?

Back

A vertical shift moves the graph up or down. For example, f(x) = x² + 5 shifts the graph of y = x² up by 5 units.

Front

What is the effect of a horizontal shift on the graph of a quadratic function?

Back

A horizontal shift moves the graph left or right. For example, f(x) = (x - 3)² shifts the graph of y = x² to the right by 3 units.

Front

What does it mean for a quadratic function to be reflected over the x-axis?

Back

A reflection over the x-axis means that the function's output values are negated. For example, f(x) = -x² is a reflection of f(x) = x².

Front

What is the parent function of a quadratic equation?

Back

The parent function of a quadratic equation is f(x) = x², which is the simplest form of a quadratic function.

Front

How do you identify the axis of symmetry in a quadratic function?

Back

The axis of symmetry can be found using the formula x = h, where (h, k) is the vertex in the vertex form f(x) = a(x - h)² + k.

Front

What is the significance of the vertex in a quadratic function?

Back

The vertex is the highest or lowest point of the parabola, depending on the direction it opens. It represents the maximum or minimum value of the function.

Front

How does changing the 'k' value in the vertex form affect the graph?

Back

Changing the 'k' value in f(x) = a(x - h)² + k results in a vertical shift of the graph. Increasing 'k' shifts the graph up, while decreasing 'k' shifts it down.

Front

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

Back

A negative 'a' value indicates that the parabola opens downward, creating a maximum point at the vertex.