Exploring Quadratic Function Transformations

What does the 'a' value in the vertex form of a quadratic function represent?

• Vertical dilation

• Horizontal translation

• Vertical translation

• Horizontal dilation

In the vertex form f(x) = a(x - h)^2 + k, what does the 'h' value represent?

• Horizontal dilation

• Vertical dilation

• Horizontal translation

• Vertical translation

If a quadratic function is transformed by adding a positive 'k' value, what happens to the graph?

• It shifts up

• It shifts right

• It shifts down

• It shifts left

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

• Compresses the graph horizontally

• Shifts the graph left or right

• Shifts the graph up or down

• Stretches the graph vertically

In the function g(x) = (x + 3)^2, what is the horizontal translation?

• 3 units down

• 3 units to the right

• 3 units to the left

• 3 units up

What happens to the graph of a quadratic function when it is reflected across the y-axis?

• All y-values become negative

• All x-values become negative

• The graph shifts down

• The graph shifts up

How is a quadratic function affected by a reflection across the x-axis?

• All x-values become negative

• All y-values become positive

• All x-values become positive

• All y-values become negative

What does a vertical stretch by a factor of 2 do to the y-values of a quadratic function?

• Doubles them

• Keeps them the same

• Halves them

• Negates them

If a quadratic function is vertically compressed by a factor of 1/2, what happens to the y-values?

• They remain the same

• They are negated

• They are halved

• They are doubled

What is the effect of a horizontal stretch by a factor of 2 on the x-values of a quadratic function?

• Doubles them

• Negates them

• Halves them

• Keeps them the same