translations of quadratic functions (midterm review)

Front

What is a translation of a function?

Back

A translation of a function is a shift of the graph of the function in a specific direction without changing its shape.

Front

How does the equation g(x) = f(x) - 4 transform f(x)?

Back

f(x) is translated down 4 units.

Front

What effect does adding a positive number to a function have?

Back

It translates the graph of the function upward.

Front

What effect does subtracting a positive number from a function have?

Back

It translates the graph of the function downward.

Front

What does the equation y = (x - 3)^2 represent?

Back

A translation of the basic quadratic function y = x^2, shifted right 3 units.

Front

What does the equation y = (x + 2)^2 represent?

Back

A translation of the basic quadratic function y = x^2, shifted left 2 units.

Front

What is the general form of a quadratic function?

Back

y = ax^2 + bx + c, where a, b, and c are constants.

Front

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

Back

Look for a constant added or subtracted from the function, affecting the y-values.

Front

What does the equation y = x^2 + 5 indicate?

Back

The graph of y = x^2 is translated up 5 units.

Front

What does the equation g(x) = x^2 - 5 indicate?

Back

The graph of y = x^2 is translated down 5 units.