1. Jeff Bivin -- LZHS Last Updated: March 11, 2008 Section 10.2

2. Jeff Bivin -- LZHS Parabola  The set of all co-planar points that are equidistant from a given point (focus) and a given line (directrix).

3. Jeff Bivin -- LZHS Parabola  The set of all points that are equidistant from a given point (focus) and a given line (directrix).

4. Jeff Bivin -- LZHS Parabola Distance between focus and vertex = p Distance between vertex and directrix = p

5. Jeff Bivin -- LZHS Parabola The line segment through the focus perpendicular to the axis of symmetry with endpoints on the parabola is called the Latus Rectum (LR) Length of the LR = 4p

6. Jeff Bivin -- LZHS Graph the following parabola y = 3x 2 + 24x + 53 y = 3(x 2 + 8x ) + 53 y + 48 = 3(x 2 + 8x + (4) 2 ) + 53 y = 3(x + 4) 2 + 5 Axis of symmetry: x = -4 Vertex: (-4, 5) y = 3(x 2 + 8x + (4) 2 ) + 53 - 48 3●(4) 2 = 48 x + 4 = 0

7. Jeff Bivin -- LZHS Graph the following parabola y = 3(x + 4) 2 + 5 Axis of symmetry: x = -4 Vertex: (-4, 5)

8. Jeff Bivin -- LZHS Graph the following parabola y = 3(x + 4) 2 + 5 Axis of symmetry: x = -4 Vertex: (-4, 5) Focus: Directrix: Length of LR:

9. Jeff Bivin -- LZHS Graph the following parabola y = -2x 2 + 12x + 11 y = -2(x 2 - 6x ) + 11 y - 18 = -2(x 2 - 6x + (-3) 2 ) + 11 y = -2(x - 3) 2 + 29 Axis of symmetry: x = 3 Vertex: (3, 29) y = -2(x 2 - 6x + (-3) 2 ) + 11 + 18 -2●(-3) 2 = -18 x - 3 = 0

10. Jeff Bivin -- LZHS Graph the following parabola y = -2(x - 3) 2 + 29 Axis of symmetry: x = 3 Vertex: (3, 29) Focus: Directrix: Length of LR:

11. Jeff Bivin -- LZHS Graph the following parabola x = y 2 + 10y + 8 x = (y 2 + 10y ) + 8 x + 25 = (y 2 + 10y + (5) 2 ) + 8 x = (y + 5) 2 - 17 Axis of symmetry: y = -5 Vertex: (-17, -5) x = (y 2 + 10y + (5) 2 ) + 8 - 25 (5) 2 = 25 y + 5 = 0

12. Jeff Bivin -- LZHS Graph the following parabola x = (y + 5) 2 - 17 Axis of symmetry: y = -5 Vertex: (-17, -5) Focus: Directrix: Length of LR:

13. Jeff Bivin -- LZHS Graph the following parabola x = -2y 2 - 8y - 1 x = -2(y 2 + 4y ) - 1 x - 8 = -2(y 2 + 4y + (2) 2 ) - 1 x = -2(y + 2) 2 + 7 Axis of symmetry: y = -2 Vertex: (7, -2) x = -2(y 2 + 4y + (2) 2 ) - 1 + 8 -2(2) 2 = -8 y + 2 = 0

14. Jeff Bivin -- LZHS Graph the following parabola x = -2(y + 2) 2 + 7 Axis of symmetry: y = -2 Vertex: (7, -2) Focus: Directrix: Length of LR:

15. Jeff Bivin -- LZHS Graph the following parabola y = 5x 2 - 30x + 46 y = 5(x 2 - 6x ) + 46 y + 45 = 5(x 2 - 6x + (-3) 2 ) + 46 y = 5(x - 3) 2 + 1 Axis of symmetry: x = 3 Vertex: (3, 1) y = 5(x 2 - 6x + (-3) 2 ) + 46 - 45 5●(-3) 2 = 45 x - 3 = 0

16. Jeff Bivin -- LZHS Graph the following parabola y = 5(x - 3) 2 + 1 Axis of symmetry: x = 3 Vertex: (3, 1) Focus: Directrix: Length of LR:

17. Jeff Bivin -- LZHS Graph the following parabola x = y 2 - 4y + 11 x = (y 2 - 8y ) + 11 x + 8 = (y 2 - 8y + (-4) 2 ) + 11 x = (y - 4) 2 + 3 Axis of symmetry: y = 4 Vertex: (3, 4) x = (y 2 - 8y + (-4) 2 ) + 11 - 8 y - 4 = 0

18. Jeff Bivin -- LZHS Graph the following parabola x = (y - 4) 2 + 3 Axis of symmetry: y = 4 Vertex: (3, 4) Focus: Directrix: Length of LR:

19. Jeff Bivin -- LZHS A Web Site & Sketchpad demo http://www.xahlee.org/SpecialPlaneCurves_dir/Parabola_dir/parabolaReflect.mov A sketchpad demo:

20. Jeff Bivin -- LZHS