Transforming Quadratic Functions

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 and a ≠ 0.

Front

What does it mean to transform a quadratic function?

Back

Transforming a quadratic function involves changing its position, shape, or orientation on the graph through operations such as translations, reflections, and stretches.

Front

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

Back

A vertical stretch occurs when the coefficient of the x² term (a) 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 of the x² term (a) is between 0 and 1, making the graph wider.

Front

How does a reflection over the x-axis affect a quadratic function?

Back

A reflection over the x-axis changes the sign of the coefficient a in the quadratic function, resulting in a graph that opens downward instead of upward.

Front

What is a translation in the context of quadratic functions?

Back

A translation is a shift of the graph of a function in a specific direction, either horizontally or vertically, without changing its shape.

Front

What does it mean to shift a graph left or right?

Back

Shifting a graph left or right involves adding or subtracting a value from the x variable in the function. For example, f(x - h) shifts the graph h units to the right.

Front

What does it mean to shift a graph up or down?

Back

Shifting a graph up or down involves adding or subtracting a value from the entire function. For example, f(x) + k shifts the graph k units up.

Front

What is the vertex of a quadratic function?

Back

The vertex is the highest or lowest point of the parabola represented by the quadratic function, depending on whether it opens upward or downward.

Front

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

Back

The vertex (h, k) can be found using the formula h = -b/(2a) and k = f(h), where f(x) is the quadratic function.