Quadratic Transformations

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

What is the equation of g?

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If f(x)=x² and g(x)=f(x - 3.4), what is the vertex of the graph g?

• (3.4, 0)

• (-3.4, 0)

• (0, 3.4)

• (0, -3.4)

The function f(x)=x² was transformed to create the function g(x)=f(x + 2) + ​ 7. What are the coordinates of the vertex of the graph of g?

Move the correct answer to each box. Not all answers will be used.

(​ (a)   ,​ (b)   )

• -2
• 7
• -7
• 0
• 2

Which answer choice describes how the graph of f(x)=x² was transformed to create the graph of n(x)=x² - 8

• A vertical shift up

• A horizontal shift to the left

• A vertical shift down

• A horizontal shift to the right

The graph of f(x)=x² was translated 6.3 units to the left to create the graph of function g. Which represents g?

• g(x)=(x - 6.3)²

• g(x)=(x + 6.3)²

• g(x)=x² - 6.3

• g(x)=x² + 6.3

The graph of quadratic parent function f was transformed to create the graph of g(x)=f(x - 2) + 5. Which graph best represents g?

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The graph of f(x)=x² was transformed to create the graph of g(x)=f(x)-11. Which statement about the graph 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 11 units to the right of the vertex of graph f

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

• The y-intercept of the graph g is 11 units below the y-intercept of the graph of f

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

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

Record your answer below.

The graph of f(x)=x² was transformed to create the graph of g(x)=(x+5.3)². Which of these describes this transformation?

• A horizontal shift to the right 5.3 units

• A horizontal shift to the left 5.3 units

• A vertical shift down 28.09 units

• A vertical shift up 28.9 units

Quadratic functions q and w are graphed on the same coordinate grid. The vertex of the graph of q is 15 units below the vertex of the graph of w. Which pair of functions could have been used to create the graphs of q and w?

• q(x)=15x² and w(x)=x²

• q(x) = x² + 15 and w(x) = x²

• q(x) = -15x² and w(x) = x²

• q(x) = x² - 15 and w(x) = x²