Transformations of Quadratic Functions

The video tutorial covers quadratic functions and their transformations, starting with the parent function y = x^2. It explains graphing, reflections, stretching, compressing, and both vertical and horizontal shifts. The tutorial concludes with combining these transformations to understand their effects on the graph.

What is the parent function for quadratic functions?

• y = x^2

• y = x

• y = x^3

• y = 2x

In the standard form of a quadratic function, what does the 'a' represent?

• The constant term

• The coefficient of x

• The coefficient of x^2

• The y-intercept

What is the vertex of the parent function y = x^2?

• (1, 1)

• (-1, 1)

• (0, 0)

• (2, 4)

What happens to the graph of y = x^2 when it is reflected?

• It stretches

• It shifts down

• It shifts up

• It flips over the x-axis

How does the graph of y = 2x^2 differ from y = x^2?

• It is flipped

• It is the same

• It is narrower

• It is wider

What does a compression do to the graph of a quadratic function?

• Makes it narrower

• Makes it wider

• Shifts it

• Flips it

What is a vertical shift in the context of quadratic functions?

• Stretching the graph

• Flipping the graph

• Moving the graph left or right

• Moving the graph up or down

How does a horizontal shift affect the graph of a quadratic function?

• Moves it up

• Flips it

• Moves it left or right

• Moves it down

What is the result of combining multiple transformations on a quadratic function?

• A single transformation

• No change

• A complex graph

• A linear graph