Quadratic Vertical and Horizontal Translations

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 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

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?

• 
• 
• 
• 

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 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?

• 
• 
• 
• 

If the quadratic parent function is to be transformed to create the graph of k(x) = f(-1/3x). What is the correct form of the equation?

The graph of quadratic function p is shown on the grid.

If m(x) = x² and p(x) = m(x) + n, what is the value of n?

• 2

• -2

• 0

• -4

The graph of a quadratic function k is shown on the grid.

If h(x) = x² and k(x) = h(x) + n, what is the value of n?

• 2

• 0

• 12

• -3