QUADRATIC FUNCTION CUBIC FUNCTION

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QUADRATIC FUNCTION CUBIC FUNCTION Name: _______________________ PART I – LINEAR TRANSFORMATIONS QUADRATIC FUNCTION General Form of the Equation: ______________________ Linear Transformations: Slide “B” to the right. Slide “B” to the left. How does changing the value of “B” affect the graph? ____________ ________________________________________________________________________________________________________ (B is a positive value) (B is a negative value) Parent Graph f(x) = x2 A = 1; B = 0; C = 0 Slide “C” to the right. Slide “C” to the left. How does changing the value of “C” affect the graph? ____________ ________________________________________________________________________________________________________ (C is a positive value) (C is a negative value) Complete Practice Problem #1A before moving on to the next Parent Graph. CUBIC FUNCTION General Form of the Equation: ______________________ Linear Transformations: Slide “B” to the right. Slide “B” to the left. How does changing the value of “B” affect the graph? ____________ ________________________________________________________________________________________________________ Parent Graph f(x) = x3 A = 1; B = 0; C = 0 (B is a positive value) (B is a negative value) Slide “C” to the right. Slide “C” to the left. How does changing the value of “C” affect the graph? ____________ ________________________________________________________________________________________________________ (C is a positive value) (C is a negative value) Complete Practice Problem #2A before moving on to the next Parent Graph.

SQUARE ROOT FUNCTION CUBE ROOT FUNCTION PART I – LINEAR TRANSFORMATIONS SQUARE ROOT FUNCTION General Form of the Equation: ______________________ Linear Transformations: Slide “B” to the right. Slide “B” to the left. How does changing the value of “B” affect the graph? ____________ ________________________________________________________________________________________________________ Parent Graph A = 1; B = 0; C = 0 (B is a positive value) (B is a negative value) Slide “C” to the right. Slide “C” to the left. How does changing the value of “C” affect the graph? ____________ ________________________________________________________________________________________________________ (C is a positive value) (C is a negative value) Complete Practice Problem #3A before moving on to the next Parent Graph. CUBE ROOT FUNCTION General Form of the Equation: ______________________ Linear Transformations: Slide “B” to the right. Slide “B” to the left. How does changing the value of “B” affect the graph? ____________ ________________________________________________________________________________________________________ Parent Graph A = 1; B = 0; C = 0 (B is a positive value) (B is a negative value) B is a negative value Slide “C” to the right. Slide “C” to the left. How does changing the value of “C” affect the graph? ____________ ________________________________________________________________________________________________________ (C is a positive value) (C is a negative value) Complete Practice Problem #4A before moving on to the next Parent Graph.

ABSOLUTE VALUE FUNCTION PART I – LINEAR TRANSFORMATIONS ABSOLUTE VALUE FUNCTION General Form of the Equation: ______________________ Linear Transformations: Slide “B” to the right. Slide “B” to the left. How does changing the value of “B” affect the graph? ____________ ________________________________________________________________________________________________________ Parent Graph f(x) = |x| A = 1; B = 0; C = 0 (B is a positive value) (B is a negative value) Slide “C” to the right. Slide “C” to the left. How does changing the value of “C” affect the graph? ____________ ________________________________________________________________________________________________________ (C is a positive value) (C is a negative value) Complete Practice Problem #5A before moving on to the next Parent Graph. RECIPROCAL FUNCTION General Form of the Equation: ______________________ Linear Transformations: Slide “B” to the right. Slide “B” to the left. How does changing the value of “B” affect the graph? ____________ ________________________________________________________________________________________________________ Parent Graph A = 1; B = 0; C = 0 (B is a positive value) (B is a negative value) Slide “C” to the right. Slide “C” to the left. How does changing the value of “C” affect the graph? ____________ ________________________________________________________________________________________________________ (C is a positive value) (C is a negative value) Complete Practice Problem #6A before moving on to the next Parent Graph.

PART II – GEOMETRIC TRANSFORMATIONS QUADRATIC FUNCTION Complete Practice Problems #1B & #1C before moving on to the next Parent Graph. Geometric Transformations: (Put “B” and “C” back to 0) Slide “A” to the left and right. What happens when “|A|” is between 0 and 1? ________________________ ________________________________________________ What happens when “A” is greater than 1? __________________________ ____________________________________________________ What happens when “A” is negative? __________________________ __________________________ A is a negative value 0 < |A| < 1 A > 1 CUBIC FUNCTION Complete Practice Problems #2B & #2C before moving on to the next Parent Graph. Geometric Transformations: (Put “B” and “C” back to 0) Slide “A” to the left and right. What happens when “|A|” is between 0 and 1? ________________________ ________________________________________________ What happens when “A” is greater than 1? __________________________ ____________________________________________________ What happens when “A” is negative? __________________________ __________________________ A is a negative value 0 < |A| < 1 A > 1 SQUARE ROOT FUNCTION Complete Practice Problems #3B & #3C before moving on to the next Parent Graph. Geometric Transformations: (Put “B” and “C” back to 0) Slide “A” to the left and right. What happens when “|A|” is between 0 and 1? ________________________ ________________________________________________ What happens when “A” is greater than 1? __________________________ ____________________________________________________ What happens when “A” is negative? __________________________ __________________________ A is a negative value 0 < |A| < 1 A > 1

PART II – GEOMETRIC TRANSFORMATIONS CUBE ROOT FUNCTION Complete Practice Problems #4B & #4C before moving on to the next Parent Graph. Geometric Transformations: (Put “B” and “C” back to 0) Slide “A” to the left and right. What happens when “|A|” is between 0 and 1? ________________________ ________________________________________________ What happens when “A” is greater than 1? __________________________ ____________________________________________________ What happens when “A” is negative? __________________________ __________________________ A is a negative value 0 < |A| < 1 A > 1 ABSOLUTE VALUE FUNCTION Complete Practice Problems #5B & #5C before moving on to the next Parent Graph. Geometric Transformations: (Put “B” and “C” back to 0) Slide “A” to the left and right. What happens when “|A|” is between 0 and 1? ________________________ ________________________________________________ What happens when “A” is greater than 1? __________________________ ____________________________________________________ What happens when “A” is negative? __________________________ __________________________ A is a negative value 0 < |A| < 1 A > 1 RECIPROCAL FUNCTION Complete Practice Problems #6B & #6C before moving on to the next Parent Graph. Geometric Transformations: (Put “B” and “C” back to 0) Slide “A” to the left and right. What happens when “|A|” is between 0 and 1? ________________________ ________________________________________________ What happens when “A” is greater than 1? __________________________ ____________________________________________________ What happens when “A” is negative? __________________________ __________________________ A is a negative value 0 < |A| < 1 A > 1

TRANSFORMATIONS PRACTICE For each example listed, first sketch the parent graph in colored pencil. Next sketch your prediction of the transformed graph on the same set of coordinate axes in regular pencil. Change the sliders in sketchpad to verify your prediction. Change your graph if necessary. QUADRATIC PRACTICE 1A) B) C) f(x) = (x + 3)2 - 2 f(x) = ½(x - 2)2 f(x) = -3x2 + 1 CUBIC PRACTICE 2A) B) C) f(x) = (x - 2)3 + 1 f(x) = -(x + 3)3 f(x) = 2x3 - 3 SQUARE ROOT PRACTICE 3A) B) C) f(x) = (x - 1)½ - 1

TRANSFORMATIONS PRACTICE For each example listed, first sketch the parent graph in colored pencil. Next sketch your prediction of the transformed graph on the same set of coordinate axes in regular pencil. Change the sliders in sketchpad to verify your prediction. Change your graph if necessary. CUBE ROOT PRACTICE 4A) B) C) ABSOLUTE VALUE PRACTICE 5A) B) C) RECIPROCAL PRACTICE 6A) B) C)