Quadratic Function Translations and Dilations

Which transformation transforms the graph of
f(x) = x² to the graph of
g(x) = (x + 4)²?

• a vertical translation 4 units up
• a vertical translation 4 units down
• a horizontal translation 4 units to the left
• a horizontal translation 4 units to the right

In the equation f(x)=5(x+3)²-10 what does transformation does the 5 cause?

• Vertical Stretch by 5

• Horizontal Compression by 5

• Reflection about the line y = 5

• Vertical Shift by 5

Which quadratic function is represented by the graph?

• y = 2(x - 4)² + 5
• y = 2(x + 4)² + 5
• y = -2(x - 4)² + 5
• y = -2(x + 4)² + 5

Tags

CCSS.HSF-IF.C.7A

John drew the graph of y= 4(x + 3)² -1. How should he transform that graph to produce the graph of y= 4(x - 6)² + 5? Select all that apply.

• Reflection over the x-axis

• Left 9

• Right 9

• Down 6

• Up 6

Which equation below is a quadratic function translated up 5 units?

• y = x² + 5
• y = (x + 5)²
• y = 5x²
• y = -x² - 5

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 

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

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.

If the function f(x) = x² is changed so that a new function is created, g(x) = 5x², how does g(x) compare to f(x)?

• The graph of g(x) is wider than the graph of f(x)

• The graph of g(x) is narrower than the graph of f(x)

• The graph of g(x) is shifted 5 units up above f(x)

• The graph of g(x) is shifted 5 units down below f(x)

Which of the following shows a vertical compression of the parent function f(x)=x²?

• y = 2x²

• y = 3/5x²

• y = -4x²

• y = -x²