Transformations and Parent Functions

Mr. M introduces transformations on linear and quadratic functions, focusing on key terms like transformation and parent graph. The video demonstrates how to use Desmos to visualize transformations by adjusting parameters in linear and quadratic equations. Viewers are encouraged to practice using Desmos and check their understanding with provided exercises. Additional resources are available for further learning.

Which of the following is NOT a type of transformation?

• Translation

• Expansion

• Rotation

• Reflection

What is the parent graph of a linear function?

• y = ax^3 + bx^2 + cx + d

• y = ax^2 + bx + c

• y = a/x

• y = mx + b

In the parent graph of a linear function, what are the default values of m and b?

• m = 0, b = 1

• m = 0, b = 0

• m = 1, b = 0

• m = 1, b = 1

What happens to the graph of a linear function when m is increased beyond 1?

• It reflects over the x-axis

• It rotates counterclockwise

• It translates upwards

• It dilates

What is the generic form of a quadratic function?

• y = ax^2 + bx + c

• y = a/x

• y = ax^3 + bx^2 + cx + d

• y = mx + b

In the parent graph of a quadratic function, what are the default values of a, b, and c?

• a = 1, b = 0, c = 0

• a = 0, b = 1, c = 0

• a = 1, b = 1, c = 1

• a = 0, b = 0, c = 1

What transformation occurs when the value of a in a quadratic function is increased beyond 1?

• The parabola reflects over the y-axis

• The parabola becomes narrower

• The parabola translates downwards

• The parabola becomes wider

Which direction does the parabola open when a is positive in a quadratic function?

• Downwards

• Upwards

• Right

• Left

What is the effect of setting b and c to zero in the parent graph of a quadratic function?

• The graph is a parabola opening upwards

• The graph becomes a straight line

• The graph is a parabola opening downwards

• The graph becomes a circle

What tool is used to explore transformations in the video?

• Graphing calculator

• Desmos

• Excel

• GeoGebra