Transformations of Quadratic Functions

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

• a translation shifting f(x) 4 units up

• a translation shifting f(x) 4 units down
• a translation shifting f(x) 4 units to the left
• a translation shifting f(x) 4 units to the right

Which transformation will occur if f(x) = x² is replaced with f(x) + 2?

• Translation left 2 units

• Narrower

• Vertical translation up by 2 units.
• Reflection across the x-axis.

Which transformation will occur if f(x) = x² is replaced with -f(x)?

• Nothing happens, it stays the same.
• Narrower

• Vertical translation up by 2 units.
• Reflection across the x-axis.

The vertex of the quadratic function f(x) in the picture is (-4, 5). If g(x) = f(x + 2) , what is the vertex of g(x)?

• (-2, 5)
• (-6, 5)
• (-4, 3)
• (-4, 7)

If the blue is f(x)=x^2, then the red must be

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

 f(x) is transformed so that it maps onto g(x). Which equation would correctly represent g(x)

• g(x)=2f(x)
• g(x)=0.5f(x)
• g(x)=f(x) + 2
• g(x)=f(x + 2)

f(x) is transformed so that it maps onto g(x). Which equation would correctly represent g(x)

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

How did we transform from f(x) =x² 
to
g(x) = -3x²

• reflection in x-axis and vertical shift down
• reflection x-axis and vertical stretch
• horizontal stretch
• reflection x-axis and vertical compression

How did we transform from the parent function?
g(x) = -1/5(x - 1)² + 7

• reflection, vertical compression, horizontal right, vertical up
• vertical compression, horizontal shift left, vertical shift up
• reflection, horizontal shift right, vertical shift down
• no changes were made to y = x²

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