Transformation of graphs HW

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 translate a graph up 5 units?

Back

Translating a graph up 5 units means shifting every point on the graph vertically upwards by 5 units.

Front

What is the parent function of a quadratic function?

Back

The parent function of a quadratic function is f(x) = x².

Front

What is a vertical stretch in graph transformations?

Back

A vertical stretch occurs when the graph of a function is stretched away from the x-axis by a factor greater than 1.

Front

How does the equation g(x) = 2x² transform the graph of f(x) = x²?

Back

The equation g(x) = 2x² represents a vertical stretch of the graph of f(x) = x² by a factor of 2.

Front

What is a horizontal translation of a graph?

Back

A horizontal translation shifts the graph left or right along the x-axis.

Front

What does the equation y = (x + 2)² represent in terms of graph transformation?

Back

The equation y = (x + 2)² represents a horizontal translation of the graph of y = x² to the left by 2 units.

Front

What is the effect of a negative sign in front of a quadratic function, such as y = -x²?

Back

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

Front

What is the difference between a vertical translation and a vertical stretch?

Back

A vertical translation shifts the graph up or down, while a vertical stretch changes the shape of the graph by stretching it away from the x-axis.

Front

What does the term 'parent function' refer to?

Back

A parent function is the simplest form of a function type, from which more complex functions can be derived.