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10.2 Parabolas JMerrill, 2010

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Review—What are Conics Conics are formed by the intersection of a plane and a double-napped cone. There are 4 basic conic sections. Notice that the plane does not pass through the vertex. If that happens, the resulting figure is a degenerate conic…

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Degenerate Conics

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Definition of the Parabola A parabola is the set of all points (x, y) in a plane that are equidistant from a fixed line (directrix) and a fixed point (focus) not on the line.

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Equations See p. 736

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Orientation State the direction in which each parabola opens (the orientation). a) b) c) d) left down up right

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Example: Find the coordinates of the vertex and focus, the equation of the directrix, and graph the parabola orientation: up vertex: (2, -3) Focus—find p (2, -2.5) directrix: y = -3.5 You will need to graph it in order to find how wide the parabola opens

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You Try orientation: right vertex: (0, 5) focus: (.25, 5) directrix: x = -.25

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Finding the Equation Find the standard form of the equation of the parabola with vertex (2, 1) and focus (2, 4) Draw what you know Is the axis of symmetry vertical or horizontal? So the model is (x - h) 2 = 4p(y – k) What is p? Equation? 3 (x - 2) 2 = 12(y – 1)

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