Transformations of Quadratic Functions Explained

What is the parent function for quadratic transformations?

• y = 1/x

• y = x^3

• y = x^2

• y = x

In the function f(x) = (x - 2)^2 + 5, what does the -2 indicate?

• Vertical translation down 2 units

• Horizontal translation left 2 units

• Horizontal translation right 2 units

• Vertical translation up 2 units

In the function f(x) = (x - 2)^2 + 5, what does the +5 indicate?

• Vertical translation down 5 units

• Horizontal translation right 5 units

• Horizontal translation left 5 units

• Vertical translation up 5 units

What is the first step in transforming the function g(x) = 2(x + 7)^2 - 6?

• Horizontal shift

• Vertical shift

• Reflection

• Vertical stretch

In the function g(x) = 2(x + 7)^2 - 6, what does the +7 indicate?

• Vertical shift down 7 units

• Horizontal shift left 7 units

• Horizontal shift right 7 units

• Vertical shift up 7 units

In the function g(x) = 2(x + 7)^2 - 6, what does the -6 indicate?

• Vertical shift down 6 units

• Horizontal shift left 6 units

• Horizontal shift right 6 units

• Vertical shift up 6 units

What does the 1/3 in the function h(x) = -1/3(x + 1)^2 + 5 indicate?

• Vertical compression by a factor of 1/3

• Horizontal compression by a factor of 1/3

• Vertical stretch by a factor of 3

• Horizontal stretch by a factor of 3

What does the negative sign in the function h(x) = -1/3(x + 1)^2 + 5 indicate?

• Vertical shift down

• Reflection over the x-axis

• Horizontal shift left

• Reflection over the y-axis

In the function h(x) = -1/3(x + 1)^2 + 5, what does the +1 indicate?

• Vertical shift down 1 unit

• Vertical shift up 1 unit

• Horizontal shift right 1 unit

• Horizontal shift left 1 unit

In the function h(x) = -1/3(x + 1)^2 + 5, what does the +5 indicate?

• Vertical shift down 5 units

• Vertical shift up 5 units

• Horizontal shift right 5 units

• Horizontal shift left 5 units