Transformations of Quadratic Functions

The quadratic parent function f(x) = x² was transformed to create function g(x). Which of the following represents function g(x)?

• g(x) = -6f(x)

• g(x) = f(x - 6)

• g(x) = f(x + 6)

• g(x) = f(x) - 6

Which card represents a shift to the left?

• g(x) = x² - 6

• h(x) = 1/2x²

• m(x) = (x + 9)²

• p(x) = (1/5x)²

Which card represents a horizontal stretch?

• g(x) = x² - 6

• h(x) = 1/2x²

• m(x) = (x + 9)²

• p(x) = (1/5x)²

Which card represents a function with a different range than f(x)?

• g(x) = x² - 6

• h(x) = 1/2x²

• m(x) = (x + 9)²

• p(x) = (1/5x)²

Function h(x) is shown on the graph. What is the equation in vertex form to represent h(x)?

• h(x) = (x - 5)² + 3

• h(x) = (x + 3)² - 5

• h(x) = (x - 2)² - 5

• h(x) = (x + 5)² - 3

Convert the equation in #5 to a standard form equation to represent h(x).

• h(x) = x² + 10x + 22

• h(x) = x² + 22x + 10

• h(x) = - x² + 10x + 22

• h(x) = x² + 4x - 4

Max is going to graph p(x) = -2(x - 6)^2 - 4 . Which of the following is NOT a true statement about the function and its graph?

• The graph will have a vertex at (6, -4).

• The graph will have a range of y < or equal to -4 .

• The axis of symmetry equation is x = 6

• The function is equivalent to

  -2x^2 + 12x - 4 .

A quadratic graph passes through the point (2, 8) and has a vertex of (-2, -4). Which of the following represents the function?

• y = 3/4 (x + 2)^2 - 4

• y = 3/4 (x - 2)^2 + 4

• y = -3/4 (x + 2)^2 + 4

• y = 4/3(x - 2)^2 - 4

The graph of f(x) = x^2 was transformed to create b(x) = -3x^2 . Which of these describes the transformation from the graph of f(x) to the graph of $ b(x) ?

• A vertical shift 3 units down

• A reflection over the x-axis and a vertical compression

• A reflection over the x-axis and a vertical stretch

• A horizontal shift 3 units to the right

The graph of the parent function f(x) = x^2 was transformed to create c(x) = f(x - 3) - 4 . Which graph best represents c(x) ?

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