By Holly Carlson. Quadratic y = x² General shape: U Domain: (-∞, ∞) Formula: a. Y= A*(x+B)² + C

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Presentation transcript:

By Holly Carlson

Quadratic y = x² General shape: U Domain: (-∞, ∞) Formula: a. Y= A*(x+B)² + C lecture/m116/functions/quadratic.gif&imgrefurl= mes/lecture/m116/functions/translations.html&usg=__Q6J3_Ivt0g4oZ0ni95E NG1jXLCo=&h=271&w=278&sz=4&hl=en&start=4&um=1&tbnid=BdlUN4wIx MgYLM:&tbnh=111&tbnw=114&prev=/images%3Fq%3Dquadratic%2Bfunction %26um%3D1%26hl%3Den Unit 2- Notes 1 “Parent Graphs & Transformations” By Miss Schmucker

Linear & Geometric Transformations Linear Transformations: a. When B is positive, it shifts to the left “B” units b. When B is negative, shifts to the right “B” units c. When C is positive, it shifts up “C” units d. When C is negative, it shifts down “C” units Geometric Transformations: a. If A is negative, the graph flips over the x- axis b. When A is between 0-1 it gets wider (closer to the x-axis) c. When A is greater than 1, it gets narrower (closer to the y-axis) Unit 2- Notes 1 “Parent Graphs & Transformations” By Miss Schmucker

Quartic y=x⁴ General shape: U Domain: (-∞,∞) Formula: a. y=A*(x+B)⁴+C Apply linear/geometric transformations Unit 2- Notes 1 “Parent Graphs & Transformations” By Miss Schmucker The quartic graph is shaped like the quadratic but is closer to the y-axis

Cubic Y = x³ General shape: S Domain: (-∞, ∞) Formula: a. Y = A * (x+B)³ + C Apply linear/geometric transformations lecture/m116/functions/quadratic.gif&imgrefurl= mes/lecture/m116/functions/translations.html&usg=__Q6J3_Ivt0g4oZ0ni95E NG1jXLCo=&h=271&w=278&sz=4&hl=en&start=4&um=1&tbnid=BdlUN4wIx MgYLM:&tbnh=111&tbnw=114&prev=/images%3Fq%3Dquadratic%2Bfunction %26um%3D1%26hl%3Den Unit 2- Notes 1 “Parent Graphs & Transformations” By Miss Schmucker

Y = x⁵ General shape: S Domain: (-∞,∞) Formula: a. y = A * (x+B)⁵+ C Apply linear/geometric transformations Unit 2- Notes 1 “Parent Graphs & Transformations” By Miss Schmucker The y=x^5 graph is shaped like the cubic graph, but is closer to the y-axis

Square Root y=√x General shape: Domain: (0,∞) Formula: y=A*(√x+B)+C Apply linear/geometric transformations rahandouts/Parent%20graph%20of%20functions%20transf.pdf Unit 2- Notes 1 “Parent Graphs & Transformations” By Miss Schmucker

Absolute Value y= |x| General shape: V Domain: (-∞,∞) Formula: a. y=A*|x+B|+C Apply linear/geometric transformations rahandouts/Parent%20graph%20of%20functions%20transf.pdf Unit 2- Notes 1 “Parent Graphs & Transformations” By Miss Schmucker

Cube Root y= ³√x General shape: Domain: (-∞,∞) Formula: a. A* (³√x+B) +C Apply linear/geometric transformations rahandouts/Parent%20graph%20of%20functions%20transf.pdf Unit 2- Notes 1 “Parent Graphs & Transformations” By Miss Schmucker

y=1/x General shape: Formula: a. y=A*(1/x+B)+C Apply linear/geometric transformations Unit 2- Notes 1 “Parent Graphs & Transformations” By Miss Schmucker Graph1OverX.jpg