Transformations of Quadratic Equation

Let the graph of g be a reflection in the x-axis of the graph of f(x) = x² - 7. Write a rule for g.

• g(x) = x² + 7

• g(x) = -x² + 7

• g(x) = -x² - 7

• g(x) = -7x²

Let the graph of g be a vertical stretch by a factor of 3 and a reflection in the x-axis of the graph of f(x) = x² + 2. Write a rule for g.

• g(x) = 3x² + 6

• g(x) = -3x² - 6

• g(x) = -3x² - 2

• g(x) = 3x² + 2

For g(x) = -x² +13, describe the transformation from the parent function.

• Reflection in x-axis, slide up 13 units

• Reflection in x-axis, slide down 13 units

• Slide up 13 units

• Slide down 13 units

For g(x) = -3(x - 6)² + 2, choose the transformation from the parent function that does NOT occur.

• Reflection in the x-axis

• Vertical stretch by factor of 3

• Slide 6 units left

• Slide 2 units up

Match the equation to its description.

• Reflected over x and up 4

• Reflected over x and down 4

• Reflected over x and right 4 

• Reflected over x and left 4

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

• Nothing happens, it stays the same.

• Vertical stretch by a factor of 2.

• 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?

• Nothing happens, it stays the same.

• Vertical stretch by a factor of 2.

• 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.

• Vertical stretch by a factor of 2.

• Vertical translation up by 2 units.

• Reflection across the x-axis.

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

What transformations have occurred? 

• Right 2 and up 2

• Left 2 and up 2

• Right 2 and down 2

• Left 2 and down 2