Graph Transformations: Focus on F(x + a) + b

The video tutorial explains the concept of graph translations, focusing on how adding constants to functions affects their graphs. It covers both vertical and horizontal shifts, emphasizing the order of operations. The tutorial uses quadratic functions as examples, highlighting the connection between transformations and completing the square. The importance of understanding these transformations for graphing and analyzing functions is stressed.

What happens to the graph of a function when a constant is added to the Y values?

• The graph reflects over the X-axis.

• The graph rotates.

• The graph shifts vertically.

• The graph shifts horizontally.

If a constant is added inside the function's brackets affecting the X values, what is the result?

• The graph shifts downwards.

• The graph shifts upwards.

• The graph shifts to the left.

• The graph shifts to the right.

In what order should transformations be applied to a graph?

• Horizontal shift first, then vertical shift.

• Vertical shift first, then horizontal shift.

• Both shifts simultaneously.

• Order does not matter.

How does the transformation of a quadratic function relate to completing the square?

• It identifies the turning point of the graph.

• It helps find the roots of the equation.

• It determines the axis of symmetry.

• It changes the degree of the polynomial.

What is the turning point of a quadratic function when expressed in the form (x + p)^2 + q?

• (-p, -q)

• (p, q)

• (p, -q)

• (-p, q)