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Transformations of Functions Viviana C. Castellón East Los Angeles College MEnTe Mathematics Enrichment through Technology

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Graph

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Given the following function, If: a > 0, then shift the graph “a” units up If:a< 0, then shift the graph “a” units down

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Given the following function, Since a > 0, then the graph will be shift up “5” units

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Let’s graph

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Given the following function, How will the graph look?

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Let’s graph

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Given the following function, Since a < 0, then the graph will be shift down “3” units

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Let’s graph

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Given the following function, How will the graph look?

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Let’s graph

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Given the following function, For this equation, b is inside the parenthesis. We get the expression and equal it to zero. If: b > 0, then shift the graph “b” units right If: b < 0, then shift the graph “b” units left

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Given the following function, We get the expression and equal it to zero. Since b < 0, then shift the graph “2” units left

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Let’s graph

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How will the graph look?

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Let’s graph

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How will the graph look?

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Let’s graph

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How will the graph look?

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Let’s graph

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Recall: a > 0 then shift up a < 0 then shift down Equal the expression to zero b > 0 then shift to the right b < 0 then shift to the left

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Let’s graph How will the graph look?

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Let’s graph

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How will the graph look?

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Let’s graph

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How will the graph look?

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Let’s graph

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How will the graph look?

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Let’s graph

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Given the following function, For this equation, c determines how wide or thin the parabola will be. if: |c|>1, then the graph is closer to the y-axis if: |c|=1, then the graph remains the same if: 0<|c|<1, then the graph is further from the y-axis if c is a negative number, then the graph will reflect on the x-axis

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Let’s graph

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Given the following function, Since |c|>1, then the graph is closer to the y-axis

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Let’s graph

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How will the graph look?

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Let’s graph

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How will the graph look?

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Let’s graph

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Recall: a>0 then shift up a<0 then shift down Equal the expression to zero b>0 then shift to the right b<0 then shift to the left if: |c|>1, then closer to the y axis if: |c|=1, then the graph is the same if: 0<|c|<1, then further from the y axis

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Let’s graph How will the graph look?

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Let’s graph

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How will the graph look?

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Let’s graph

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How will the graph look?

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Let’s graph

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How will the graph look?

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Let’s graph

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Congratulations!! You just completed the transformation of

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Transformations Review Vertex form: y = a(x – h) 2 + k The vertex form of a quadratic equation allows you to immediately identify the vertex of a parabola.

Transformations Review Vertex form: y = a(x – h) 2 + k The vertex form of a quadratic equation allows you to immediately identify the vertex of a parabola.

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