Transformations of Quadratic Functions

The video tutorial introduces transformations of quadratic functions, focusing on vertical and horizontal translations, as well as reflections over the x-axis and y-axis. It explains how to move parabolas up, down, left, and right by adjusting the function's equation. The concept of HIO (Horizontal Inside Opposite) is introduced for horizontal transformations. Reflections are discussed, highlighting the visual changes when reflecting over the x-axis and the lack of change over the y-axis for parabolas. Practical examples are provided to illustrate these transformations.

What is the primary focus of transformations in quadratic functions?

• Changing the color of the graph

• Altering the size and location of the parabola

• Modifying the equation to a linear function

• Transforming the function into a circle

How does adding a positive number at the end of a quadratic function affect its graph?

• Moves the graph to the left

• Moves the graph to the right

• Moves the graph upwards

• Moves the graph downwards

What happens to a parabola when a negative number is added at the end of its function?

• It shifts upwards

• It shifts downwards

• It shifts to the right

• It shifts to the left

In horizontal translations, what does a negative number inside the parentheses indicate?

• The graph moves to the left

• The graph moves upwards

• The graph moves downwards

• The graph moves to the right

What is the effect of a positive number inside the parentheses in horizontal translations?

• The graph moves to the left

• The graph moves to the right

• The graph moves upwards

• The graph moves downwards

What transformation occurs when a negative sign is placed in front of a quadratic function?

• The parabola shifts to the right

• The parabola reflects over the y-axis

• The parabola reflects over the x-axis

• The parabola becomes a circle

How does reflecting a parabola over the y-axis affect its appearance?

• It looks different from the parent function

• It becomes a straight line

• It remains visually unchanged

• It becomes a circle

What is the term used for moving a graph up or down?

• Vertical translation

• Reflection

• Rotation

• Horizontal translation

Tags

CCSS.HSF.BF.B.3

What does the acronym 'HIO' stand for in the context of transformations?

• Horizontal is inside and opposite

• Horizontal is outside

• Height is optimal

• Height is outside

What is the effect of a reflection over the x-axis on a parabola?

• It becomes a happy parabola

• It becomes a sad parabola

• It shifts to the left

• It shifts to the right