Transformations of Quadratic Functions

The video tutorial explains how the graph of f(x) = x^2 is transformed to create the graph of g(x) = f(x) - 9. The transformation involves a vertical shift down by 9 units. The instructor demonstrates this by substituting f(x) with x^2 and graphing both functions. A table of values is used to illustrate the shift, and the y-intercept's change is analyzed. The tutorial concludes with a summary of the transformation process.

What is the initial function f(x) that is being transformed?

• f(x) = x^2

• f(x) = x^3

• f(x) = x + 9

• f(x) = x - 9

What is the expression for G(x) after substituting f(x)?

• G(x) = x^2 + 9

• G(x) = x^2 - 9

• G(x) = x^2

• G(x) = x^2 + x

What type of transformation is applied to the graph of f(x) to obtain G(x)?

• Rotation

• Reflection

• Horizontal shift

• Vertical shift

How many units is the graph of f(x) shifted to create G(x)?

• 11 units

• 7 units

• 5 units

• 9 units

What is the y-value for x = 0 in the table of values for f(x) = x^2?

• 0

• 9

• 4

• 1

What is the y-value for x = 2 in the table of values for f(x) = x^2?

• 1

• 4

• 9

• 0

What is the y-value for x = -1 in the table of values for f(x) = x^2?

• 1

• 0

• 9

• 4

What is the y-value for x = 0 in the table of values for G(x) = x^2 - 9?

• 0

• -5

• -1

• -9

What operation is performed on the y-values of f(x) to obtain the y-values of G(x)?

• Multiply by 9

• Add 9

• Divide by 9

• Subtract 9

What is the y-value for x = 2 in the table of values for G(x) = x^2 - 9?

• -5

• -4

• -9

• -8