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Worksheet Key

Worksheet Key. Shape of a parabola from a cone. Real-Life Examples. Definitions. Parabola: Graph of a quadratic equation to which a set of points in a plane that are the same distance from a given point Vertex: Midpoint of the graph; the turning point

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Worksheet Key

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  1. Worksheet Key 11.3: Parabolas

  2. 11.3: Parabolas

  3. Shape of a parabola from a cone 11.3: Parabolas

  4. Real-Life Examples 11.3: Parabolas

  5. Definitions Parabola:Graph of a quadratic equation to which a set of points in a plane that are the same distance from a given point Vertex:Midpoint of the graph; the turning point Focus:Distance from the vertex; located inside the parabola Directrix:A fixed line used to define its shape; located outside of the parabola Axis of Symmetry:A line that divides a plane figure or a graph into congruent reflected halves. Latus Rectum:A line segment through the foci of the shape in which it is perpendicular through the major axis and endpoints of the ellipse Eccentricity:Ratio to describe the shape of the conic, e = 1 11.3: Parabolas

  6. Formulas to know: Horizontal Axis Standard Form: If the ‘x’ is not being squared: 11.3: Parabolas

  7. Formulas to know: Vertical Axis Standard Form: If the ‘y’ is not being squared: 11.3: Parabolas

  8. Formulas to know: All Standard Form Equations 11.3: Parabolas

  9. Review of Parent Function Parabolas y = x2 or x2 = y x = y2 or y2 = x 11.3: Parabolas

  10. The Parabola Brief Clip Where do we see the focus point used in real-life? 11.3: Parabolas

  11. Horizontal Parabola Vertex: (h, k) Focus point: (p, 0) Directrix: x = –p Axis of Symmetry: y = k Length of Latus Rectum: |4p| Latus Rectum: (h + p, k+ 2p) Horizontal parabola due to its ‘Axis of Symmetry’ (h, k) F (p, 0) y = k x = –p 11.3: Parabolas

  12. Vertical Parabola Vertex: (h, k) Focus point: (0, p) Directrix: y = –p Axis of Symmetry: x = k Length of Latus Rectum: |4p| Latus Rectum: (h+ 2p, k + p) (p, 0) F (h, k) y = –p Vertical parabola due to its ‘Axis of Symmetry’ x = k 11.3: Parabolas

  13. Review of Parent Function Parabolas y = x2 or x2 = y x = y2 or y2 = x 11.3: Parabolas

  14. Steps in Writing Conic Sections of Parabolas • Identify whether the equation opens Up/Down or Left/Right • Divide the coefficient (if necessary) to keep the variable by itself • On the side without the squared into the equation (which usually is a fraction), drop off all the variables • Multiply the coefficient (not involved with squared) with ¼ to solve for p • Put it in standard form and graph 11.3: Parabolas

  15. Example 1 Determine the vertex, focus point, directrix, axis of symmetry, latus rectum, and graph the parabola for y = 4x2. First, figure out what variable is squared? Put into the suitable equation. What is the vertex? (0, 0) 11.3: Parabolas

  16. Example 1 Determine the vertex, focus point, directrix, axis of symmetry, latus rectum, and graph the parabola for y = 4x2. To find p: Isolate the equation to where the variable squared has a coefficient of 1. 11.3: Parabolas

  17. Example 1 Determine the vertex, focus point, directrix, axis of symmetry, latus rectum, and graph the parabola for y = 4x2. To find p: Take the coefficient in front of the isolated un-squared variable and multiply it by ¼ 11.3: Parabolas

  18. Example 1 Determine the vertex, focus point, directrix, axis of symmetry, latus rectum, and graph the parabola for y = 4x2. To determine the Latus Rectum: 11.3: Parabolas

  19. Example 1 Determine the vertex, focus point, directrix, axis of symmetry, latus rectum, and graph the parabola for y = 4x2. (0, 0) 1/16 Vertex: P: Focus Point: Directrix: Axis of Symmetry: Latus Rectum: (0, 1/16) F y = –1/16 x = 0 (+1/8, 1/16) 11.3: Parabolas

  20. Example 2 Determine the vertex, focus point, directrix, axis of symmetry, latus rectum, and graph the parabola for x = (–1/8)y2. (0, 0) –2 Vertex: P: Focus Point: Directrix: Axis of Symmetry: Latus Rectum: (–2, 0) F x = 2 y = 0 (–2, +4) 11.3: Parabolas

  21. Your Turn Determine the vertex, focus point, directrix, axis of symmetry, latus rectum, and graph the parabola for x = (1/20)y2. (0, 0) 5 Vertex: P: Focus Point: Directrix: Axis of Symmetry: Latus Rectum: (5, 0) F y = –5 x = 0 (5, +10) 11.3: Parabolas

  22. Example 3 Write in standard form equation of a parabola with the vertex is at the origin and the focus is at (2, 0). F P = 2 11.3: Parabolas

  23. Your Turn Write a standard form equation of a parabola where the directrix is y = 6 and focus point (0, –6). 11.3: Parabolas

  24. Example 4 Determine the vertex, focus point, directrix, axis of symmetry, latus rectum, and graph the parabola for (y + 1)2 = 8(x + 1). (–1, –1) 2 Vertex: P: Focus Point: Directrix: Axis of Symmetry: Latus Rectum: (1, –1) x = –3 F y = 1 (1, 3), (1, –5) 11.3: Parabolas

  25. Example 5 Determine the vertex, focus point, directrix, axis of symmetry, latus rectum, and graph the parabola for (x – 7)2 = –8(y – 2). (7, 2) –2 Vertex: P: Focus Point: Directrix: Axis of Symmetry: Latus Rectum: (7, –2) y = 4 F x = 7 (7, 5), (7, 9) 11.3: Parabolas

  26. Your Turn Determine the vertex, focus point, directrix, axis of symmetry, latus rectum, and graph the parabola for (y – 1)2 = –4(x – 1). (1, 1) –1 Vertex: P: Focus Point: Directrix: Axis of Symmetry: Latus Rectum: (0, 1) F x = 2 y = 1 (0, 3), (0, –1) 11.3: Parabolas

  27. Example 6 Write an standard form equation of a parabola where the vertex is (–7, –3) and focus point (2, –3). F 11.3: Parabolas

  28. Example 7 Write an standard form equation of a parabola where the vertex is (–2, 1) and the directrix is at x = 1. 11.3: Parabolas

  29. Your Turn Write an standard form equation of a parabola where the axis of symmetry is at y = –1, directrix is at x = 2 and the focus point (4, –1). 11.3: Parabolas

  30. Converting to Standard Form • Identify whether it is an ellipse by using the equation, b2 – 4acwhere the answer is equal to zero using the equation, Ax2 + Bxy + Cy2 + Dx + Ey + F = 0 • Rearrange variables for x’s and y’s through factoring • Take GCF and add everything to other side • Use completing the square; using what’s added to the x’s and y’s is added to the radius • Identify the coefficient which is raised to the first power and divide the term by 2 • Take the second term, divide the term by 2, and square that number • Add to both sides to the equation • Put the equation into factored form • Put it in standard form 11.3: Parabolas

  31. Example 8 Change the equation y2 – 9x + 16y + 64 = 0 to standard form. 11.3: Parabolas

  32. Example 8 Change the equation y2 – 9x + 16y + 64 = 0 to standard form. 11.3: Parabolas

  33. Example 8 Change the equation y2 – 9x + 16y + 64 = 0 to standard form. 11.3: Parabolas

  34. Example 9 Change the equation x2 + 14x – 12y + 97 = 0 to standard form. 11.3: Parabolas

  35. Your Turn Change the equation y2 – 16x – 6y + 73 = 0 to standard form. 11.3: Parabolas

  36. Assignment Worksheet 11.3: Parabolas

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