Quadratic TRansformations

The graph f(x) = x² was translated 7.5 units to the left to create the graph of function g. Which function represents g?

• g(x) = x² + 7.5

• g(x) = x² – 7.5

• g(x) = (x + 7.5)²

• g(x) = (x – 7.5)²

The graph f(x) = x² was transformed to create the graph of g(x) = f(x) - 6. Which statement about the graphs is true?

• The graph of g is a reflection of the graph of f across the x-axis.

• The vertex of the graph of g is 6 units to the right of the vertex of the graph of f.

• The graph of g is a reflection of the graph of f across the y-axis.

• The y-intercept of the graph of g is 6 units below the y-intercept of the graph of f.

If f(x) = x² and g(x) = f(x + 5.7), what is the vertex of the graph of g?

• (5.7, 0)

• (− 5.7, 0)

• (0, 5.7)

• (0, − 5.7)

The quadratic function f(x) = x² is transformed to create g as shown in the graph. What is the equation of g?

• g(x) = f(x + 3) – 2

• g(x) = f(x + 2) – 3

• g(x) = f(x – 3) + 2

• g(x) = 2f(x – 3) + 2

The quadratic parent function f(x) = x² was transformed to create the graph below. Describe its transformation.

• A) A vertical shift up 4 units

• B) A vertical shift down 4 units

• C) A horizontal shift to the right 2 units.

• D) A horizontal shift to the left 2 units.

The graph f(x) = x² was transformed to create the graph of g(x) = f(x + 10). Which of these describes the transformation?

• A) A horizontal shift to the left 10 units.

• B) A horizontal shift to the right 10 units.

• C) A vertical shift up 10 units.

• D) A vertical shift down 10 units.

The graph f(x) = x² was transformed to create the graph of g(x) = (x – 3)². Which of these describes the transformation?

• A) A horizontal shift to the right 3 units.

• B) A horizontal shift to the left 3 units.

• C) A vertical shift down 9 units.

• D) A vertical shift up 9 units.

The graph f(x) = x² was transformed to create the graph of g(x) = f(x) + 2. Which statement about the graphs is true?

• The graph of g is a reflection of the graph of f across the y-axis.

• The graph of g is a reflection of the graph of f across the x-axis.

• The vertex of the graph of g is 2 units above the y-intercept of the graph of f.

• The y-intercept of the graph of g is 2 units to the right of the vertex of the graph of f.

If f(x) = x² and g(x) = f(x – 2.3)², what is the vertex of the graph of h?

• (–2.3, 0)

• (0, 2.3)

• (0, –2.3)

• (2.3, 0)

The graph f(x) = x² was transformed 3 units right to create the graph of function g. Which function represents g?

• g(x) = (x - 3)²

• g(x) = (x + 3)²

• g(x) = x² + 3

• g(x) = x² - 3