Exploring Quadratic Transformations

The video tutorial covers quadratic transformations, focusing on how variables a, b, h, and k affect the graph of a quadratic function. It explains vertical and horizontal stretches, compressions, and reflections, as well as shifts in the graph. The tutorial includes practice questions to reinforce understanding of these transformations.

What is the parent function of a quadratic equation?

• y = 1/x

• y = x

• y = x^3

• y = x^2

What effect does a positive 'a' value greater than 1 have on a quadratic graph?

• Horizontal stretch

• Reflection over the x-axis

• Vertical compression

• Vertical stretch

What does a negative 'a' value cause in the graph of a quadratic equation?

• Reflection over the x-axis

• Reflection over the y-axis

• Horizontal compression

• Vertical stretch

If 'B' is less than 1, what happens to the graph?

• Horizontal compression

• Horizontal stretch

• Vertical stretch

• Vertical compression

What does a negative 'B' value do to the graph?

• Causes vertical compression

• Reflects over the y-axis

• Reflects over the x-axis

• Causes horizontal stretch

What is the effect of 'H' being negative in the quadratic transformation?

• Shifts left

• Shifts up

• Shifts right

• Shifts down

How does 'K' affect the position of the graph when it is positive?

• Moves down

• Moves left

• Moves right

• Moves up

What does a vertical stretch imply about the graph's appearance?

• It becomes narrower and taller

• It moves to the right

• It moves to the left

• It becomes wider and shorter

If 'a' is a fraction between 0 and 1, what is the effect on the graph?

• Reflection over the x-axis

• Vertical compression

• Horizontal compression

• Vertical stretch

What transformation occurs when 'K' is negative?

• Shifts down

• Shifts up

• Shifts left

• Shifts right