Quadratic Transformation

Which statement explains the difference between the graphs of f(x) = 5x² and g(x) = -10x²?

• The graph of g(x) is obtained by flipping f(x) over the y-axis and stretching vertically by a factor of 2.

• The graph of g(x) is obtained by flipping f(x) over the x-axis and compressing vertically by a factor of 2.

• The graph of g(x) is obtained by flipping f(x) over the x-axis and stretching vertically by a factor of 2.

• The graph of f(x) is obtained by flipping g(x) over the y-axis and compressing vertically by a factor of 2.

Which describes the effect of the transformations on the graph of ƒ(x) = x² when changed to ƒ(x) = 4(x + 1)² − 7?

• stretched vertically, shifted left 1 units, and shifted down 7 units

• stretched vertically, shifted right 1 units, and shifted up 7 units

• compressed vertically, shifted left 1 units, and shifted down 7 units

• compressed vertically, shifted right 1 units, and shifted up 7 units

What is the function g(x) created from f(x) = x² by moving the graph right 3 units, vertically stretching it by a factor of 2, and shifting the graph down 5 units?

• g(x) = 2(x + 3)² + 5

• g(x) = 2(x - 3)² - 5

• g(x) = 3(x - 5)² - 2

• g(x) = 2(x - 5)² - 3

What is the function g(x) created from f(x) = x² by moving the graph right 3 units, adding vertical compression by a factor of 1/2, and shifting the graph up 1 unit?

• g(x) = 2(x + 3)² + 1

• g(x)= 1/2(x -3)² + 1

• g(x)= 1/2(x +3)² - 1

• g(x)= 1/2(x -1)² + 3

What is the effect on the graph of the function f(x) = x² when f(x) is changed to f(7x)?

• stretched vertically

• compressed vertically (shrink)

• stretched horizontally

• compressed horizontally (shrink)

What is the effect on the graph of the function f(x) = x² when f(x) is changed to f(1/2x)?

• stretched vertically

• compressed vertically

• stretched horizontally

• compressed horizontally

The graph of the equation y = 2x² - 5 is shown.

Which equation will shift the graph up 7 units?

• y = 2(x + 7)²

• y = 2x² + 2

• y = 2x² - 2

• y = 2x² + 7

Which graph shows f(x) = x² reflected over the x-axis?

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What transformation occurs if the quadratic function y = (x - 2)^2 is changed to y = (x - 2)^2 - 5?

• Shift 5 units to the right.

• Shift 5 units to the left.

• Shift 5 units upwards.

• Shift 5 units downwards.

Which of the following is a transformation that results in a narrower parabola compared to y = (x)^2?

• y = 0.5(x)^2

• y = 2(x)^2

• y = (x)^2 + 3

• y = (x)^2 - 3