Exploring Transformations of Quadratic Functions

What does the 'h' in the quadratic function g(x) = (x - h)^2 + k represent?

• Stretch factor

• Horizontal translation

• Reflection

• Vertical translation

In the function g(x) = (x - 1)^2 - 3, what is the vertex of the parabola?

• (-1, 3)

• (1, 3)

• (1, -3)

• (-1, -3)

If a quadratic function has a negative sign in front of the x term, what type of reflection does it represent?

• Reflection over the y-axis

• Vertical stretch

• No reflection

• Reflection over the x-axis

What happens to the graph of a quadratic function when it is multiplied by a factor greater than 1?

• It stretches horizontally

• It shrinks vertically

• It shrinks horizontally

• It stretches vertically

How do you determine if a transformation is a horizontal stretch or shrink?

• By using the reciprocal of the multiplication factor

• By checking if the multiplication factor is less than 1

• By adding the multiplication factor to the x term

• By checking if the multiplication factor is greater than 1

What is the first step in writing a transformation rule for a quadratic function?

• Applying horizontal translation

• Applying vertical translation

• Simplifying the equation

• Identifying reflections

In the transformation process, what does adding a negative value to the x term represent?

• Moving the graph right

• Moving the graph left

• Moving the graph down

• Moving the graph up

What is the effect of a vertical translation on a quadratic function?

• It changes the width of the parabola

• It moves the graph left or right

• It moves the graph up or down

• It reflects the graph over the x-axis

When applying a reflection over the y-axis, what part of the quadratic function is affected?

• The entire function

• Only the x term

• Only the y term

• The constant term

What is the final step in the transformation process of a quadratic function?

• Applying horizontal translation

• Identifying reflections

• Applying vertical translation

• Simplifying the equation