Quadratic Transformations

The graph of m(x) = x² was transformed to create the graph of n(x) = x² + 21.  Which of these describes the transformation?

• A vertical shift down 21 units.
• A vertical shift up 21 units.
• A horizontal shift to the right 21 units.
• A horizontal shift to the left 21 units.

Tags

CCSS.HSF.BF.B.3

CCSS.HSG.CO.A.2

Quadratic functions f and g are graphed.  Graph g is narrower than the graph of f.  Which pair of functions could have been used to create the graphs of f and g?

• g(x) = (0.5x)² and f(x) = x²  
• g(x) = (5x)² and f(x) = x² 
• g(x) = 5x² and f(x) = x² 
• g(x) = (x + 5)² and f(x) = x² 

The graph of g(x) = x² is transformed to create the graph of g(x) = -g(x).  Describe the transformation.

• Vertical shift up.
• Horizontal shift to the right.
• Reflection in the x-axis.
• Horizontal shift to the left.

Tags

CCSS.HSF.BF.B.3

CCSS.HSG.CO.A.4

The graph of g(x) = x² is transformed to create the graph of h(x) = 0.5g(x).  Describe the transformation.

• Vertical stretch by a factor of 0.5.
• Vertical shrink/compression by a factor of 0.5
• Horizontal stretch by a factor of 0.5.
• Horizontal shrink/compression by a factor of 0.5.

Quadratic function f(x)=x² is graphed on a coordinate plane.  The graph of a new    quadratic is formed by changing the vertex to (3, 0).  Which function could represent the new quadratic? 

• g(x) = x² - 3
• g(x) = (x - 3)²
• g(x) = x² + 3
• g(x) = (x + 3)²

Tags

CCSS.HSF.BF.B.3

CCSS.HSA.CED.A.2

Which two transformations can be used to obtain the graph of h(x)= -x² - d from the    function f(x) = x²?

• A reflection across the x-axis followed by a translation up d units.
• A reflection across the x-axis followed by a translation down d units.
• A reflection across the y-axis followed by a translation to the right d units.
• A reflection across the y-axis followed by a translation to the left d units.