Exploring Transformations of Quadratic Functions

What is the vertex form of a quadratic function?

• F(x) = a(x - h)^2 + k

• F(x) = a(x - h)^2 - k

• F(x) = a(x + h)^2 + k

• F(x) = ax^2 + bx + c

If the vertex form of a quadratic function is F(x) = a(x - h)^2 + k, what is the axis of symmetry?

• y = h

• x = k

• x = h

• y = k

In the vertex form F(x) = a(x - h)^2 + k, what does a positive 'h' indicate?

• The graph shifts to the left

• The graph shifts downward

• The graph shifts to the right

• The graph shifts upward

What does a negative 'k' in the vertex form F(x) = a(x - h)^2 + k indicate?

• The graph shifts downward

• The graph shifts upward

• The graph shifts to the right

• The graph shifts to the left

If a quadratic function has a positive 'a' value, what is the direction of the parabola?

• Upward

• Downward

• Leftward

• Rightward

What type of transformation occurs when 'a' is greater than 1 in the vertex form?

• Vertical stretch

• Vertical compression

• Horizontal compression

• Horizontal stretch

If the negative sign is outside the parentheses in the vertex form, what type of reflection occurs?

• Reflection over the x-axis

• Reflection over the y-axis

• Reflection over both axes

• No reflection

In the function G(x) = -3(x - 1)^2 - 2, what does the '-3' indicate?

• Horizontal stretch and reflection over the x-axis

• Vertical compression and reflection over the y-axis

• Horizontal compression and reflection over the y-axis

• Vertical stretch and reflection over the x-axis

How does the graph of G(x) = 1/3(x + 4)^2 - 1 transform from the parent function?

• Stretched vertically, shifted right 4 units, and up 1 unit

• Compressed vertically, shifted left 4 units, and down 1 unit

• Stretched horizontally, shifted right 4 units, and up 1 unit

• Compressed horizontally, shifted left 4 units, and down 1 unit

Why is the vertex form useful in identifying transformations?

• It simplifies the equation

• It provides clear information about shifts, stretches, and reflections

• It eliminates the need for graphing

• It only applies to quadratic functions