Quadratic Transformations

Which describes the transformation from 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

What transformation will occur if f(x) = x² is changed to 2⋅f(x)?

• Wider

• 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) + 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

• Yes, "+3" on the end of the function moves the function right 3 units

• No, "+3" on the end of the function moves the function left 3 units

• No, "+3" on the end of the function moves the function down 3 units

• No, "+3" on the end of the function moves the function up 3 units

The graph of f(x) is transformed into g(x). Which equation correctly represents g(x)

• g(x)=f(x - 3)

• g(x)=f(x) - 3

• g(x)=f(x) + 3

• g(x)=3f(x)

The graph of f(x) is transformed into g(x). Which equation correctly represents g(x)

• g(x)=2f(x)

• g(x)=0.5f(x)

• g(x)=f(x) + 2

• g(x)=f(x + 2)

The graph of f(x) is transformed into g(x). Which equation correctly represents g(x)?

• g(x)=f(x + 3)

• g(x)=f(x - 3)

• g(x)=f(x) + 3

• g(x)=f(x) - 2