Introduction to Conic sections and transformation of graphs
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The document discusses different conic sections and graph transformations. It defines circles, ellipses, parabolas, and hyperbolas as the shapes that result from cutting a cone with different planes. It also explains that a translation moves a graph horizontally by adding or subtracting a value from x, and vertically by adding or subtracting a value from y. Translations shift the entire function up, down, left or right without changing its shape.
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3) Axis of symmetry which is an axis around which the cube can rotate through some angle while remaining unchanged.
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Introduction to Conic sections and transformation of graphs
- 1. Conic Sections and Transformation of Graphs
- 5. Circle A set of all points having the same distance (the radius) from a given point on the circle.
- 6. Circle A Circle is formed if the plane is parallel to the base of the cone
- 7. Ellipse a regular oval shape, traced by a point moving in a plane so that the sum of its distances from two other points (the foci) is constant, or resulting when a cone is cut by an oblique plane which does not intersect the base.
- 8. Ellipse An ellipse is formed when the tilted plane intersects only one cone to form a bounded curved
- 9. Parabola a symmetrical open plane curve formed by the intersection of a cone with a plane parallel to its side.
- 10. Parabola A parabola is formed when a plane is parallel to the slanting height of the cone
- 11. Hyperbola a symmetrical open curve formed by the intersection of a circular cone with a plane at a smaller angle with its axis than the side of the cone.
- 12. Hyperbola A hyperbola is formed when the plane (not necessarily vertical) intersects both cones to form an unbounded curves
- 13. Translation of Graphs Suppose a graph whose equation is given, is translated, that is moved horizontally and or/ vertically. The translated graph equation can be determined as follows: 1. If the graph is translated h>0 units to the right, replace all x with x - h 2. If the graph is translated h>0 units to the left, replace all x with x + h 3. If the graph is translated k>0 units upwards, replace all y with y - k 1. If the graph is translated k>0 units downwards, replace all x
- 14. A Translation is a Transformation in which the entire function is shifted upward, downward, to the left or right.
- 16. Examples