Understanding Graph Transformations

The video tutorial explains how to determine the equation of a transformed graph, g(x), based on the known graph of y = x^2, f(x). It covers recognizing transformations such as reflection across the x-axis, and determining if there is any vertical or horizontal stretch or compression. The tutorial also discusses how to identify shifts in the graph's vertex and calculate the values of transformation parameters A, C, and D. Finally, it derives the equation for the transformed graph, g(x), as a reflection and shift of f(x).

What is the initial step in determining the equation for the transformed graph?

• Calculating the slope

• Identifying the type of transformation

• Determining the domain

• Finding the y-intercept

What does it mean if a graph opens down instead of up?

• The graph is shifted left

• The graph is compressed

• The graph is reflected across the x-axis

• The graph is stretched

What is the value of A if the graph is reflected across the x-axis?

• 0

• 2

• -1

• 1

What indicates that there is no vertical or horizontal stretch or compression?

• The graph is shifted right

• The graph opens up

• The shape of the parabola remains unchanged

• The vertex is at the origin

How is the vertex of the blue parabola different from the red one?

• It is at the origin

• It is shifted right and up

• It is at the point (-1,-3)

• It is at the point (1,3)

What is the significance of the vertex being at (-1,-3)?

• It suggests a reflection across the y-axis

• It confirms the graph's shift left and down

• It shows a horizontal compression

• It indicates a vertical stretch

What does a positive value of C indicate about the graph's shift?

• The graph is shifted right

• The graph is shifted left

• The graph is shifted up

• The graph is shifted down

What does a negative value of D indicate about the graph's shift?

• The graph is shifted right

• The graph is shifted left

• The graph is shifted down

• The graph is shifted up

What is the final equation for the transformed graph G(x)?

• G(x) = -(x - 1)^2 + 3

• G(x) = (x - 1)^2 - 3

• G(x) = -(x + 1)^2 - 3

• G(x) = (x + 1)^2 + 3

What transformation occurs if the graph is shifted left one unit?

• D is negative

• D is positive

• C is negative

• C is positive