Conic Sections

Mrs Lenox Math Help: Conic Sections

Horizontal Ellipse

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Start by finding the center(h,k). Then from the center go left and right a units to locate thevertices . From the center, go up and down b units to locate the covertices. The vertices are always the pair furthest away from the center. The foci are inside the vertices. Use the formula to find c, then go left and right that number of units from the center to put the foci dots on the graph.

Domain graph graph

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Vertical Ellipse

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Start by finding the center(h,k). Then from the center go up and down b units to locate thevertices . From the center, go left and right a units to locate the covertices. The vertices are always the pair furthest away from the center. The foci are inside the vertices. Use the formula to find c, then go up and down that number of units from the center to put the foci dots on the graph.

Intercepts graph

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Horizontal Hyperbola

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Start by finding the center(h,k). Then from the center go left and right a units to locate thevertices. Draw vertical lines at the vertices. From the center, go up and down b units to locate horizontal lines to draw a box. Asymptotes can be drawn by putting lines diagonally through the corners of the box.The hyperbola branches are two U shapes that go out from the vertices and do not cross the asymptotes you drew. The foci are inside the vertices. Use the formula to find c, then go left and right that number of units from the center to put the foci dots on the graph.

Range graph

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Vertical Hyperbola

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Start by finding the center(h,k). Then from the center go up and down a units to locate thevertices. Draw horizontal lines at the vertices. From the center, go left and right b units to locate vertical lines to draw a box. Asymptotes can be drawn by putting lines diagonally through the corners of the box.The hyperbola branches are two U shapes that go out from the vertices and do not cross the asymptotes you drew. The foci are inside the vertices. Use the formula to find c, then go up and down that number of units from the center to put the foci dots on the graph.

Absolute value graph

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Horizontal Parabola

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Start by finding the vertex(h,k). If 4p is positive,it opens towards positive infinity. If 4p is negative it opens towards negative infinity. The focus is inside the vertex. Use the formula to find p, then go left or right that number of units from the vertex to put the focus on the graph.

Increasing graph

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Vertical Hyperbola

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Start by finding the vertex(h,k). If 4p is positive,it opens towards positive infinity. If 4p is negative it opens towards negative infinity. The focus is inside the vertex. Use the formula to find p, then go up or down that number of units from the vertex to put the focus on the graph.

maximum graph

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Practice Problems

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