1. (Math 3) 5.7: Use Figures in Three-Dimensional Space Unit 2: Polynomial Functions MM3G3a: Plot the point (x, y, z) and understand it as a vertex of a rectangular prism. b: Apply the distance formula in 3-space. c: Recognize and understand equations of planes and spheres.

2. 3-Space: x, y and z axis 8 octants (x,y,z) Distance:

3. Ex. Graph. 1. A (-2,-3,1) 2. B (0,2,-2) 3. C (1,0,-2) 4. D (2,-1,3)

4. Ex. Graph the equation. 5. 3x + 2y + 4z = 126. x + 2y - 4z = 16

5. Ex. Find the distance between the points. 7. (1,0,-2); (2,-1,3)8. (3,2,0),(0,-1,3)

6. Sphere:

7. Ex. Write an equation of the sphere in standard form with the given center and radius. 9. (8,-2,0); r = 1210. (10,-2,3); r=

8. Ex. Complete the square to write the equation of the sphere in standard form. 11. x 2 + y 2 + z 2 + 9x - 2y + 10z = -10.25

9. 12. 4x 2 + 4y 2 + 4z 2 - 4x - 32y + 8z + 33 = 0

10. Homework: Pg. 207 #1(graph points only), #2(graph points only), #3-11odd, 22 Pg. 208 # 9-19odd, 20