11.3 Quadratic Transformations

The graph of f(x) = x² is transformed to create the graph of g(x) = f(x + 7). Which description best describes the transformation.

• The graph of f is vertically translated 7 units up to create the graph of g.

• The graph of f is vertically translated 7 units down to create the graph of g.

• The graph of f is horizontally translated 7 units right to create the graph of g.

• The graph of f is horizontally translated 7 units left to create the graph of g.

The quadratic parent function f(x) = x² is to be vertically stretched by a factor of 3 and horizontally translated 5 units right to create the graph of g. Which function shows this transformation?

• g(x) = 3f(x) - 5

• g(x) = 3f(x) + 5

• g(x) = 3f(x - 5)

• g(x) = 3f(x + 5)

The graph of f(x) = x² was transformed to create the graph of t(x) = (x + 4)². Which of these describes this transformation?

• A vertical translation down 4 units

• A vertical translation up 4 units

• A horizontal translation to the left 4 units

• A horizontal translation to the right 4 units

The graph shows the quadratic parent function (dashed) and a transformation p. Which quadratic function best represents the graph of p?

• p(x) = (x + 1)² + 4

• p(x) = (x + 1)² - 4

• p(x) = (x - 1)² + 4

• p(x) = (x - 1)² - 4

Tags

CCSS.HSA.SSE.A.1

CCSS.HSA.SSE.A.2

CCSS.HSA.SSE.B.3

CCSS.HSF.IF.B.4

CCSS.HSF.IF.C.7

The graph of f(x) = x² (dashed) is transformed to create the graph of m(x) = -3f(x + 2). Which graph best represents f and m?

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The graph of f(x) = x² is transformed to create the graph of h(x) = -1/5f(x - 1) + 7. Which description best describes the transformation?

• The graph of f is vertically compressed by a factor of 5, horizontally translated 1 unit right, vertically translated 7 units up, and reflected over the x-axis to create h.

• The graph of f is vertically stretched by a factor of 5, horizontally translated 1 unit right, vertically translated 7 units down, and reflected over the x-axis to create h.

• The graph of f is vertically compressed by a factor of 5, horizontally translated 1 unit left, vertically translated 7 units up, and reflected over the x-axis to create h.

• The graph of f is vertically stretched by a factor of 5, horizontally translated 1 unit right, vertically translated 7 units up, and reflected over the y-axis to create h.

The graph of f(x) = x² is transformed to create the graph of w(x) = (x + 2)² - 4. Which of these best describes the transformation

• A horizontal translation to the right 2 units and a vertical translation up 4 units

• A horizontal translation to the right 2 units and a vertical translation down 4 units

• A horizontal translation to the left 2 units and a vertical translation up 4 units

• A horizontal translation to the left 2 units and a vertical translation down 4 units

The quadratic parent function f(x) = x² is to be horizontally compressed by a factor of 5 and reflected over the y-axis to create the graph of c. Which function best represents this transformation?

• c(x) = -1/5f(x)

• c(x) = -5f(x)

• c(x) = f(-5x)

• c(x) = f(-1/5x)

The graph of f(x) = x² (dashed) is transformed to create the graph r. Which function best represents r?

• r(x) = -4(x + 3)²

• r(x) = -4(x - 3)²

• r(x) = -1/4(x + 3)²

• r(x) = -1/4(x - 3)²

The graph of f(x) = x² (dashed) is transformed to create the graph of v(x) = f(3x) - 5. Which graph best represents f and v?

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