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Functions and Transformations

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This investigation is about how different parabolas, hyperbolas, exponential graphs can be manipulated to produce images. Explanations of these graphs and their respective transformations are also present.

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Functions and Transformations
Topics this document covers:
Geometry Algebraic geometry Mathematics Conic sections Parabolas Ellipse Analytic geometry Cylinder The Method of Mechanical Theorems Quadratic equation
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Topics this document covers:
Geometry Algebraic geometry Mathematics Conic sections Parabolas Ellipse Analytic geometry Cylinder The Method of Mechanical Theorems Quadratic equation
Sample Text:
2(x − 2)2 − 0.8 , therefore T. P: (2, -0.8) Parabola 2 (BLUE): - Since y=0 is the horizontal line of symmetry of the two restricted parabolas, the y-values of the points along Parabola 2 are the same as Parabola 1, multiplied by -1. Therefore, the equation for Parabola 2 : −y = 0.2(x − 2)2 − 0.8 - This can be written as : y = −0.2(x − 2)2 + 0.8 - It can be seen that the T.P of Parabola 2 is (2,0.8) ALGEBRA TO DETERMINE TAIL END-POINTS Parabola 1 (RED): We know the equation : y = 0.2(x − 2)2 − 0.8, so by substituting y=0.8 (since we want the top of the tail to have the same vertical position a...
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