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Algebra 2: Unit #6 (6.8 NOTES)Name: ___________________________6.8 Graphing Radical Equations, Solving by GraphingBlock: ___________Big Idea: The graph of a radical function is made by a series of transformations to the parent functions y=x or y=3x. These values (a, h, k) to the same transformations on quadratics and reciprocal functions.Quadratic Function: y=ax-h2+k Reciprocal Function: y=ax-h+kSquare Root Function:y=ax-h+kCube Root Function: y=a3x-h+kRecall: What transformations do the values a, h, and k do to the parent function? Be specific, include direction!ahkTo graph radicals, translate the points of the parent function. Remember the order matters: “ABC Order!” Reflection (across x-axis) Stretch/Compression Translation (shifting horizontal/vertical)left28210500Part I: Graphing Square Root Functions: The parent function y=x is graphed.Use a different color to graph each transformed function. Identify the domain and range for each!right99585y=x-3Domain: __________ Range: ___________y=x+4Domain: __________ Range: ___________y=x-7Domain: __________ Range: ___________y=x +5Domain: __________ Range: ___________y=-2xDomain: __________ Range: ___________y=12xDomain: __________ Range: ___________y=-3x+2+5Domain: __________ Range: ___________00y=x-3Domain: __________ Range: ___________y=x+4Domain: __________ Range: ___________y=x-7Domain: __________ Range: ___________y=x +5Domain: __________ Range: ___________y=-2xDomain: __________ Range: ___________y=12xDomain: __________ Range: ___________y=-3x+2+5Domain: __________ Range: ___________Writing: How do the domain and range of square root functions relate to the transformations? How can you tell the domain and range from the rule without graphing?-27360231308300362140574930y=3x+2Domain: __________ Range: ___________y=3x-1Domain: __________ Range: ___________y=3x-6Domain: __________ Range: ___________y=3x+8Domain: __________ Range: ___________y=-143xDomain: __________ Range: ___________y=53xDomain: __________ Range: ___________y=-43x+3-2Domain: __________ Range: ___________00y=3x+2Domain: __________ Range: ___________y=3x-1Domain: __________ Range: ___________y=3x-6Domain: __________ Range: ___________y=3x+8Domain: __________ Range: ___________y=-143xDomain: __________ Range: ___________y=53xDomain: __________ Range: ___________y=-43x+3-2Domain: __________ Range: ___________Part II: Graphing Cube Root Functions: The parent function y=3x is graphed. Use a different color to graph each transformed function. Identify the domain and range for each!Writing: Why are the domain and range of all cubic functions the same? What other radical equations would have this domain and range?Part III: Solving a Radical Equation By Graphing (calculator allowed thank Baby Gabel!)On a graph, if two functions are equal, this will appear as an _______________________. In the table, his will look like ______________________________. Therefore, we can graph each side of an equation as a separate equation (Y1= ____ and Y2 = _____) and find this/these point(s)!(x+3)=4x-2B. 3x-1=x-1Part IV: Rewriting a Radical FunctionRewrite each function so that it is in the form y=a1x-h+k or y=a31x-h+k using factoring, perfect squares/cubes, etc. Then describe all the transformations made to the parent function. C. y=36x-72+4D. y=3-8x-32-2E. y=x+716+3Bookwork: page 418: For #17-20 (just describe the transformations), then do #21-23, 33, 35, 36, 45, 46, 49, 52, 60 ................
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