9_2 - Section 9.2: The Parabola Instructor: Ms. Hoa Nguyen

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Section 9.2: The Parabola Instructor: Ms. Hoa Nguyen (nguyen@scs.fsu.edu) 1 Parabola Definition In Section 3.1, we have learned that the graph of a quadratic function is a parabola. In this section, we will understand the relation between the geometry of the parabola and the quadratic equation. Definition of a Parabola : Given a line D ( directrix ) and a point F ( focus ) not on D , the set of all points P such that d ( P,F ) = d ( P,D ) is called a parabola . Note: d ( A,B ) denotes the distance from A to B : d ( A,B ) = p ( x A - x B ) 2 + ( y A - y B ) 2 . The line through the focus F and orthogonal (perpendicular) to the directrix D is called the axis of symmetry of the parabola. The point where the parabola intersects with its axis of symmetry is called the vertex V. 2 Find the Equation of the Parabola Case 1: The directrix is vertical, and the vertex is at the origin ( a > 0 ). 1
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Table 1: Equations of a Parabola: The directrix is vertical, and the vertex is at the origin. Directrix
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9_2 - Section 9.2: The Parabola Instructor: Ms. Hoa Nguyen

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