Transformations on Quadratic Functions Vertex Form

In the vertex form f(x) = a(x - h)² + k , what does the 'k' value do?

• Shifts the function left or right

• Reflects over the x-axis

• Vertical stretch or compression

• Shifts the function up or down

Given f(x) = ax² , if 0 < a < 1 , the graph will transform by

• becoming wider or vertically compressed

• becoming narrower or vertically stretched

The graph of f(x) = x² was transformed to create the graph of g(x) = (x - 7.5)². Which of these describes this transformation?

• F.) A horizontal shift to the right 7.5 units.

• G.) A horizontal shift to the left 7.5 units.

• H.) A vertical shift down 56.25 units.

• J.) A vertical shift up 56.25 units.

• H.) g(x) = x²- 4.5

• J.) g(x) = x² + 4.5

The graph of f(x) = x² is transformed to create the graph of h(x) = 2f(x). Which graph best represents f and h?

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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) - 9. 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 9 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 9 units below the y-intercept of the graph of f.

• F.) A reflection over the x-axis and a horizontal stretch

• G.) A reflection over the y-axis and a horizontal stretch

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

• J.) A reflection over the y-axis and a vertical stretch

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?