Understanding Parabolas: Equations, Properties, and Graphing Techniques
This lesson covers the standard equations of parabolas, focusing on definitions, properties, and graphing techniques. Students will fill out tables for quadratic equations, plot parabolas, and learn how to identify important features like the focus, directrix, and axis of symmetry. Example problems from the textbook illustrate these concepts, providing clarity and practice. Students will engage in required and additional practice problems to reinforce their understanding and complete a homework assignment to apply their skills.
Understanding Parabolas: Equations, Properties, and Graphing Techniques
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Presentation Transcript
Warm-Up Question For each equation, fill the table and then plot.
Quadratic Relations and Conic Sections Equations of Parabolas
Standard Equation of a Parabola • Lesson: P.490 The standard form of the equation of a parabola with vertex at (0, 0) is as follows: EquationFocusDirectrixAxis of Symmetry (0, p) y = -p Vertical (x = 0) (p,0) x = -p Horizontal (y = 0) Refer to page 496 of the textbook for diagrams. • Example: P.497 Identify the focus, directrix, and axis of symmetry of parabola . Required Practice: P.498 – G.P. 1, 4; P.499 – 15, 21 Additional Practice: P. 499 17, 19
Writing an equation of a parabola • Example: P.498 Write the standard form of the equation of the parabola with vertex at (0, 0) and the given directrix or focus. 1) 2) Required Practice: P.499 – 26, 29, 34, 36; P.500 – 39, 40, 48, 50 Additional Practice: P.499 – 35, 37; P.500 – 47, 49
Homework Assignment Workbook page 101 - 102 4, 5, 7, 8, 10, 12, 13, 15, 16, 17, 20, 21
