PHHSTransformations of Quadratic Functions

Front

What is a transformation in the context of quadratic functions?

Back

A transformation refers to the changes made to the graph of a function, such as shifts, reflections, stretches, or compressions.

Front

What does shifting a graph 4 units to the left mean?

Back

It means that every point on the graph of the function is moved 4 units in the negative x-direction.

Front

How does the function g(x) = (x + 4)² relate to f(x) = x²?

Back

g(x) is the result of shifting the graph of f(x) = x² 4 units to the left.

Front

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

Back

It reflects the graph across the x-axis.

Front

What does it mean for a quadratic function to be 'narrower'?

Back

A quadratic function is narrower when the absolute value of the leading coefficient is greater than 1.

Front

What is the vertex of a quadratic function?

Back

The vertex is the highest or lowest point on the graph of a quadratic function, depending on its orientation.

Front

How do you identify a vertical shift in a quadratic function?

Back

A vertical shift is indicated by a constant added or subtracted from the function, such as f(x) = x² + k.

Front

What transformation occurs in the function g(x) = -3x²?

Back

This function reflects the graph of f(x) = x² across the x-axis and makes it narrower.

Front

What does the function f(x) = (x - 3)² represent?

Back

It represents a translation of the graph of f(x) = x² 3 units to the right.

Front

How can you tell if a quadratic function has been shifted up or down?

Back

If a constant is added to the function, it shifts up; if subtracted, it shifts down.