Transforming the Eight Parent Graphs. Vertical Compression Vertical Dilations Vertical Stretch Transform! (Click Me)

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Presentation transcript:

Transforming the Eight Parent Graphs

Vertical Compression Vertical Dilations Vertical Stretch Transform! (Click Me)

The Parameters for Graphing Form ( h, k ): The Key Point The value of a Positive: Same OrientationIf it Increases: Vertical Stretch Negative: FlippedIf it Decreases: Vertical Compression Parent Graph: When a=1, h=0, and k=0 They do the same thing for every function!

Graphing Form for the First 5 Parent Graphs ( h, k ): The Key Point The value of a Positive: Same OrientationIf it Increases: Vertical Stretch Negative: FlippedIf it Decreases: Vertical Compression Parent Graph: When a=1, h=0, and k=0 QuadraticCubic HyperbolaSquare Root Exponential

Quadratic Function Parent Equation Graphing Form

Example: Quadratic New Equation: y = 4 x = 3 Transformation: Shift the parent graph three units to the right and four units up. (3,4)

Cubic Function Parent Equation Graphing Form

Example: Cubic y = 5 x = 0 Transformation: Flip the parent graph and shift it five units up. New Equation: Transformation: (0,5)

Hyperbolic Function Parent Equation Graphing Form

Example: Hyperbola y = -3 x = -4 Transformation: Shift the parent graph four units to the left and three units down. New Equation: Transformation: (-4,-3)

Square Root Function Parent Equation Graphing Form

Example: Square Root y = 0 x = -6 Transformation: Shift the parent graph six units to the left. New Equation: Transformation: (-6,0)

Exponential Function Example of a Parent Equation Graphing Form

Example: Exponential y = 2 x = 5 a = 3 Transformation: Shift the parent graph five units to the right and two units up. Then stretch the graph by a factor of 3. New Equation: Transformation: (5,2)

Linear Function Parent Equation Graphing Form Unless specified, you do not need to have the answer in y=mx+b form! Point: Slope: (h,k)(h,k)

Example: Linear y = 4 x = -6 Slope = ½ Transformation: A line with slope ½ that passes through the point (-6,4). New Equation: Slope Point (-6,4)

Absolute Value Function Parent Equation Graphing Form Absolute value can be found in the calculator: a)MATH b)Right to NUM c) 1. abs(

Example: Absolute Value y = 4 x = -3 Transformation: Flip the parent graph and shift it three units to the left and four units up. Transformation: New Equation: (-3,4)

Equation for a Circle Example Graphing Form Center: Radius: (0,0) Center: Radius: (h,k)(h,k)

Example: Circle y = -1 x = 4 Transformation: A circle centered at (4,-1) whose radius is 4. Transformation: New Equation: Center: Radius: (4,-1) NO!Is a circle a function? (4,-1)