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 function?

Back

Transforming a function involves changing its position, shape, or size on a graph through operations such as shifting, stretching, or reflecting.

Tags

CCSS.HSF.BF.B.3

Front

What is the effect of a vertical stretch on a quadratic function?

Back

A vertical stretch occurs when the coefficient of x² (a) is greater than 1, making the graph narrower.

Front

What is the effect of a vertical shrink on a quadratic function?

Back

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

Front

How does adding a constant to a function affect its graph?

Back

Adding a constant to a function shifts the graph vertically. If the constant is positive, the graph shifts up; if negative, it shifts down.

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 term 'horizontal shift' refer to in function transformations?

Back

A horizontal shift refers to moving the graph left or right. This is achieved by adding or subtracting a value inside the function's argument.

Front

What is the effect of a negative coefficient in front of a quadratic function?

Back

A negative coefficient reflects the graph of the function across the x-axis.

Tags

CCSS.HSF-IF.C.7A

Front

How do you represent a function that is shifted two units to the right?

Back

To shift a function f(x) two units to the right, the new function is f(x - 2).

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.