Exploring Quadratic Transformations

The video tutorial explains how different transformations affect the graph of the function x squared. It covers the impact of the 'a' value on the graph's orientation and shape, including reflections and stretches. The tutorial also discusses how compression and stretching occur when the absolute value of 'a' is less than or greater than one. It further explores horizontal and vertical shifts caused by changes in the inside and outside values, respectively. The video concludes with examples of analyzing and listing transformations.

What happens to the graph of a quadratic function when the 'a' value is positive?

• The graph reflects over the x-axis.

• The graph becomes narrower.

• The graph shifts to the right.

• The graph opens upwards.

What does a negative 'a' value indicate about the direction of a quadratic graph?

• It remains unchanged.

• It shifts to the left.

• It opens downwards.

• It becomes wider.

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CCSS.HSF-IF.C.7A

What effect does an 'a' value greater than 1 have on the graph of a function?

• Stretching by a factor less than the 'a' value.

• Compression by a factor of the 'a' value.

• No change to the graph.

• Stretching by a factor of the 'a' value.

How does a compression affect the appearance of a graph when 'a' is less than 1?

• Makes it reflect over the x-axis.

• Makes it wider.

• Makes it unchanged.

• Makes it skinnier.

What does a negative inside value do to the graph's horizontal position?

• Makes it narrower.

• No movement.

• Moves it right.

• Moves it left.

If the inside value of a function is positive, in which direction does the graph move?

• Moves right.

• Moves left.

• Moves up.

• Moves down.

What happens to the graph when the outside value is negative?

• Becomes narrower.

• Shifts down.

• Shifts up.

• No change.

How does a positive outside value affect the graph's vertical position?

• Moves it downwards.

• Reflects it over the x-axis.

• Moves it upwards.

• Makes it wider.

What transformation occurs when the 'a' value is negative and absolute value greater than 1?

• Shift to the right.

• Stretch and reflection.

• Compression and reflection.

• No transformation.

What is the effect of a negative inside value on the graph's horizontal movement?

• Shifts it to the right.

• No movement.

• Shifts it to the left.

• Makes it wider.