Understanding Graph Transformations

The video tutorial explains how to determine the equation of a transformed graph. Starting with the basic graph of y = x^2, the tutorial identifies transformations such as vertical compression and horizontal shift. It explains how to determine the values of transformation parameters a and c, using a point on the graph to solve for a. The final equation for the transformed graph is derived as g(x) = 1/2(x - 3)^2.

What is the initial function used as a reference for the transformation?

• y = x^3

• y = x

• y = 2x

• y = x^2

Which transformation is selected to explain the change in the graph's width?

• Vertical stretch

• Horizontal shift

• Horizontal compression

• Vertical compression

What does a vertical compression imply about the value of 'a' in the transformation equation?

• a = 1

• a > 1

• a < 1

• a = 0

How is the graph shifted if the vertex moves from the origin to (3, 0)?

• Right 3 units

• Left 3 units

• Up 3 units

• Down 3 units

What is the value of 'c' if the graph is shifted right by 3 units?

• c = 3

• c = -3

• c = 0

• c = 1

Which point is used to calculate the value of 'a' in the transformation equation?

• (0, 0)

• (5, 2)

• (3, 0)

• (2, 5)

What is the value of 'a' after solving the equation using the point (5, 2)?

• a = 2

• a = 1

• a = 3

• a = 1/2

What is the final equation for the transformed graph?

• g(x) = (x - 3)^2

• g(x) = 2(x - 3)^2

• g(x) = 1/2(x + 3)^2

• g(x) = 1/2(x - 3)^2

What does the negative sign in 'x - 3' indicate about the graph's shift?

• Shift right

• Shift down

• Shift left

• Shift up

What is the significance of not selecting the vertex point for solving 'a'?

• Vertex point is always zero

• Vertex point is irrelevant

• Vertex point does not provide enough information

• Vertex point is not on the graph