Exploring Quadratic Transformations

What does a change inside the parentheses of a function indicate?

• Vertical shift

• Reflection over the y-axis

• No change

• Horizontal shift

If there is a '+5' inside the parentheses of a function, in which direction does the graph shift?

• Down 5 units

• Up 5 units

• Right 5 units

• Left 5 units

What does a negative value outside the parentheses being multiplied indicate about the graph?

• Shift to the right

• Reflection over the x-axis

• Reflection over the y-axis

• Shift to the left

In the function 'y = (x - 2)^2 + 1', what is the effect of the '-2' inside the parentheses?

• Moves right 2 units

• Moves left 2 units

• Moves down 2 units

• Moves up 2 units

What does the '+1' outside the parentheses in 'y = (x - 2)^2 + 1' cause the graph to do?

• Move down 1 unit

• Move up 1 unit

• Move right 1 unit

• Move left 1 unit

How does the absolute value of 'a' being less than one affect the graph of a quadratic function?

• Makes it taller

• No change

• Makes it wider

• Makes it narrower

What happens to the graph if the absolute value of 'a' is greater than one?

• It shifts to the left

• It becomes wider

• It becomes narrower

• It shifts to the right

If 'a' is negative in a quadratic function, what additional transformation occurs?

• Reflection over the y-axis

• Reflection over the x-axis

• Shift downwards

• Shift upwards

In the function 'y = (x + 3)^2 - 4', what does the '-4' outside the parentheses do?

• Moves the graph up 4 units

• Moves the graph down 4 units

• Moves the graph left 4 units

• Moves the graph right 4 units

What is the effect of a '+3' inside the parentheses of 'y = (x + 3)^2'?

• Shifts the graph up 3 units

• Shifts the graph down 3 units

• Shifts the graph right 3 units

• Shifts the graph left 3 units