1. 1. [latex]\begin{array}{lc}B&\left(0,1\right)\\F&1\\C\;or\;D\;\;&x=1\\C\;or\;D&x=1\\A&\left(1,0\right)\\E&y=1\end{array}[/latex]

1. 2. [latex]y=3[/latex]
   3. [latex]x=3[/latex]
   4. [latex](-3,0)[/latex]

1. 5. Explain
   6. [latex]-4[/latex]
   7. [latex]-\frac32[/latex]
   8. [latex]4[/latex]
      1. [latex]-\frac56[/latex]
      2. [latex]\frac12[/latex]
      3. [latex]-10[/latex]
      1. [latex]57[/latex]
      2. [latex]5[/latex]
      3. [latex]\frac{19}2[/latex]
      1. [latex]-26[/latex]
      2. [latex]-2[/latex]
      3. [latex]4[/latex]
      1. [latex]-13[/latex]
      2. [latex]-\frac{89}{16}[/latex]
      3. [latex]-\frac{41}4[/latex]

13. 13. An intercept is a point where a graph touches the x- or y-axis.
        1. y-intercept: (0, 2); x-intercept: (-5, 0)
        2. y-intercept: (0, -2); x-intercepts: (-2, 0), (1, 0)

13. 15. 1. Yes
        2. No

16. Infinity and negative infinity; Discuss with classmates.

1. 1
2. none
3. 1

Graph A

1. [latex]x=3[/latex]
2. [latex](3,4)[/latex]
3. maximum
4. Domain [latex]=\left(-\infty,\infty\right);[/latex] Range [latex]=(-\infty,4\rbrack[/latex]
5. [latex](0,-5)[/latex]
6. The points are symmetric across the axis of symmetry.

Graph B

1. [latex]x=-2[/latex]
2. [latex](-2,-5)[/latex]
3. maximum
4. D [latex]=\left(-\infty,\infty\right);[/latex] R [latex]=\lbrack-5,\infty)[/latex]
5. [latex](0,-1)[/latex]
6. The points are symmetric across the axis of symmetry.

• 4. Up
     Axis of symmetry: [latex]x=3[/latex]
     Vertex: [latex](3,4)[/latex]
     y-intercept: [latex](0,13)[/latex]
     Number of x-intercepts: none
     Domain : [latex]\left(-\infty,\infty\right)[/latex]
     Range: [latex]\lbrack4,\infty)[/latex]
  5. Down
     Axis of symmetry: [latex]x=-1[/latex]
     Vertex: [latex](-1,0)[/latex]
     y-intercept: [latex](0,-1)[/latex]
     Number of x-intercepts: 1
     Domain : [latex]\left(-\infty,\infty\right)[/latex]
     Range: [latex](-\infty,0\rbrack[/latex]
  6. Down
     Axis of symmetry: [latex]x=2[/latex]
     Vertex: [latex](2,7)[/latex]
     y-intercept: [latex](0,3)[/latex]
     Number of x-intercepts: 2
     Domain : [latex]\left(-\infty,\infty\right)[/latex]
     Range: [latex](-\infty,7\rbrack[/latex]
  7. Down
     Axis of symmetry: [latex]x=-5[/latex]
     Vertex: [latex](-5,-7)[/latex]
     y-intercept: [latex](0,-82)[/latex]
     Number of x-intercepts: none
     Domain : [latex]\left(-\infty,\infty\right)[/latex]
     Range: [latex](-\infty,-7\rbrack[/latex]

1. Explain.
2. Up
   Axis of symmetry: [latex]x=-5[/latex]
   Vertex: [latex](-5,1)[/latex]
   y-intercept: [latex](0,26)[/latex]
   Number of x-intercepts: none
   Domain : [latex]\left(-\infty,\infty\right)[/latex]
   Range: [latex]\lbrack1,\infty)[/latex]
3. Down
   Axis of symmetry: [latex]x=2[/latex]
   Vertex: [latex](2,8)[/latex]
   y-intercept: [latex](0,0)[/latex]
   Number of x-intercepts: 2
   Domain : [latex]\left(-\infty,\infty\right)[/latex]
   Range: [latex](-\infty,8\rbrack[/latex]
   Explain.
4. Down
   Axis of symmetry: [latex]x=-4[/latex]
   Vertex: [latex](-4,0)[/latex]
   y-intercept: [latex](0,-16)[/latex]
   Number of x-intercepts: 1
   Domain : [latex]\left(-\infty,\infty\right)[/latex]
   Range: [latex](-\infty,0\rbrack[/latex]
   Explain.
5. Down
   Axis of symmetry: [latex]x=-1[/latex]
   Vertex: [latex](1,-2)[/latex]
   y-intercept: [latex](0,-3)[/latex]
   Number of x-intercepts: none
   Domain : [latex]\left(-\infty,\infty\right)[/latex]
   Range: [latex](-\infty,-2\rbrack[/latex]
6. Up
   Axis of symmetry: [latex]x=-4[/latex]
   Vertex: [latex](4,-2)[/latex]
   y-intercept: [latex](0,30)[/latex]
   Number of x-intercepts: 2
   Domain : [latex]\left(-\infty,\infty\right)[/latex]
   Range: [latex]\lbrack-2,\infty)[/latex]
7. Answers may vary.

1. 1. meters per second
   2. 58.8 m
   3. [latex]D\left(t\right)=-4.9t^2+19.6t+58.8[/latex]
   4. The distance from the ground in meters
   5. When does the object strike the ground?
   1. feet per second
   2. height above the ground
   3. feet
   4. time
   5. seconds
   6. the graph is a parabola opening down.
   1. seconds
   2. meters
   3. seconds
   1. feet
   2. seconds

5. Discuss
6. exact
7. approximate
8. exact
9. approximate
10. exact
11. approximate
12. [latex]=[/latex]
13. [latex]\approx[/latex]
14. [latex]\approx[/latex]
15. [latex]=[/latex]
16. [latex]\approx[/latex]
17. [latex]\approx[/latex]
18. [latex]\approx[/latex]
19. [latex]=[/latex]
20. [latex]\approx[/latex]
21. [latex]3,600[/latex]
22. [latex]45[/latex]
23. [latex]39.82[/latex]
24. [latex]72.49[/latex]
25. [latex]-3.094[/latex]
26. [latex]0.3[/latex]
27. [latex]0.3[/latex]
28. [latex]0.59[/latex]

1. 1. 8 sec
   2. 256 ft
      1. 192 ft
      2. Up
      1. 192 ft
      2. Down
   3. 1 second, 7 seconds
   4. from 0 to 1 because it covered more distance.
   5. Domain [latex]=\left[0,8\right][/latex]; Range [latex]=\left[0,256\right][/latex]
   1. [latex](0,0)[/latex]
   2. Discuss
   3. Discuss
   4. x-intercept is used for domain; vertex is used for range

   1. x	y
      0	23
      3	311
      6	311
      9	23
      10	−137

   2. 23 ft
   3. 311 ft
   4. 347 ft
   5. between 9 and 10 secs
   1. 2 meters
   2. [latex]2.30625[/latex] meters
   3. The ball is never above 3 meters
2. The skateboarder is about 0.86 ft above the ground at the bottom of the half-pipe. The bottom of the half-pipe is 6.75 ft away from the starting point of the ride.
   1. 25 feet
   2. 25 feet at [latex]t=0[/latex]
   1. No, the maximum height is [latex]12.25[/latex] feet.
   2. 6 feet

1. 1. x	y
      0	80
      1	124
      2	136
      3	116
      4	64
      5	−20

   2. 80 ft
   3. 134 ft
   4. 136.25 ft
   5. between 4 and 5 seconds
   1. 8 feet
   2. 0.625 seconds
   3. 14.25 feet
   1. [latex](0, 0)[/latex]
   2. Discuss
   3. Discuss
   4. x-intercept is used for domain; vertex is used for range
   5. Answers may vary
   1. 33 feet
   2. 0.375 seconds
   3. 35.25 feet
   1. There are 4,540 parking spaces at 7 A.M.
   2. There are only 40 parking spaces at 10 A.M.
2. The maximum height is 52 meters at time [latex]t=0[/latex]

1. 1. 1. 5
      2. 10
      3. [latex]\sqrt{889}[/latex]
      4. Discuss with a classmate

      ---

      5. [latex]2\sqrt{3}[/latex]
      6. [latex]6\sqrt{2}[/latex]
      7. [latex]\frac{7 \pm \sqrt{3}}{2}[/latex]
      8. [latex]-1, 7[/latex]
      9. [latex]1 \pm \sqrt{5}[/latex]
      10. [latex]\frac{5\pm\sqrt5}2[/latex]

1. 11. [latex]6i[/latex]
   12. [latex]6i\sqrt{2}[/latex]
   13. [latex]\frac{2}{5}i[/latex]
   14. [latex]-3 \pm \frac{3}{2}i[/latex]
   15. [latex]\frac{5}{2} \pm \frac{3\sqrt{2}}{2}i[/latex]
   16. [latex]2 \pm 3i[/latex]

1. 1. 1. [latex]x = 2 \pm \sqrt{7}[/latex]
      2. [latex]x = \pm i\sqrt{3}[/latex]
      3. [latex]x = \frac{-5 \pm \sqrt{33}}{2}[/latex]
      4. [latex]x = \frac{3}{2} \pm \frac{\sqrt{11}}{2}i[/latex]
      5. [latex]x = -3[/latex]
      6. [latex]x = \frac{3 \pm \sqrt{13}}{4}[/latex]
      7. [latex]x = \frac{3 \pm \sqrt{29}}{10}[/latex]
      8. [latex]x = \frac{7}{2} \pm \frac{\sqrt{23}}{2}i[/latex]
      9. [latex]x = \pm \frac{5}{2}i[/latex]
      10. [latex]x = 4, -\frac{1}{2}[/latex]
      11. [latex]x = \frac{-1 \pm \sqrt{11}}{4}[/latex]
      12. [latex]x = \frac{9}{2}, 0[/latex]

      ---

      13. 2
      14. 1
      15. none
      16. Discuss.
      17. Check with your classmate.

1. 1. 18. Down
          Axis of symmetry: [latex]x=1[/latex]
          Vertex: (1,3)
          y-intercept: (0,1)
          x-intercepts: [latex]\left(\frac{2\pm\sqrt6}2,0\right)[/latex]
          Domain: [latex]\left(-\infty,\infty\right)[/latex]
          Range: [latex](-\infty,3\rbrack[/latex]

1. 19. 1. 293 feet
       2. 329 feet
       3. 2 seconds, 7 seconds
       4. 9.03 seconds
       5. Domain [latex]=[0,9.03][/latex]; Range [latex]=0,329[/latex]
   20. ~2.33 sec

1. 1. 1. [latex]5\sqrt{7}[/latex]
      2. [latex]3 \pm \frac{\sqrt{3}}{2}[/latex]
      3. [latex]10i\sqrt{3}[/latex]
      4. [latex]5 \pm \frac{i\sqrt{30}}{2}[/latex]

      ---

      5. [latex]x = \frac{7}{2}, -\frac{5}{3}[/latex]
      6. [latex]x = \frac{17}{20}, -\frac{10}{29}[/latex]
      7. [latex]x = \frac{5 \pm \sqrt{109}}{6}[/latex]
      8. [latex]x = \pm \frac{\sqrt{2}}{4}[/latex]
      9. [latex]x = 4 \pm \sqrt{6}[/latex]
      10. [latex]x = -\frac{3}{4} \pm \frac{\sqrt{51}}{4}i[/latex]
      11. [latex]x = \frac{1}{3} \pm \frac{\sqrt{71}}{3}i[/latex]
      12. [latex]x = 1[/latex]
      13. [latex]x = \frac{5 \pm \sqrt{17}}{2}[/latex]
      14. [latex]x = 0, 2[/latex]
      15. Explain.
      16. Discuss.
      17. Check with a classmate.

1. 1. 18. Down
          Axis of symmetry: [latex]x=3[/latex]
          Vertex: (3,3)
          y-intercept: (0,-15)
          x-intercepts: [latex]\left(\frac{6\pm\sqrt6}2,0\right);[/latex]
          Domain: [latex]\left(-\infty,\infty\right)[/latex]
          Range: [latex](-\infty,3\rbrack[/latex]

1. 19. 1.57 seconds
   20. 1.45 seconds
   21. [latex]\approx10.32[/latex] seconds longer
       1. 2 seconds
       2. 382 feet
       3. Domain [latex]=[0,4.763][/latex]; Range [latex]=[0,382][/latex]
       4. 

1. 1. [latex]x = \pm 4[/latex]
   2. [latex]x = \pm 10[/latex]
   3. [latex]x = \pm 5i[/latex]
   4. [latex]x = \pm 9i[/latex]
   5. [latex]x = \pm i\sqrt{3}[/latex]
   6. [latex]x = \pm i[/latex]
   7. [latex]x = \pm \sqrt{15}[/latex]
   8. [latex]x = \pm \frac{3\sqrt{11}}{2}[/latex]
   9. [latex]x = \pm 4[/latex]
   10. [latex]x = \pm \frac{2\sqrt{2}}{7}i[/latex]
   11. [latex]x = \pm 2\sqrt{3}[/latex]
   12. [latex]x = \pm \sqrt{41}[/latex]
   13. [latex]x = \pm \sqrt{3}[/latex]
   14. [latex]x = \pm \sqrt{23}[/latex]
   15. [latex]x = \pm 8[/latex]
   16. [latex]x = \pm \frac{2}{3}i[/latex]

   ---

   17. 1.25 seconds
   18. [latex]x=\pm\frac{\sqrt5}3[/latex]
   19. Explain.
   20. Discuss.

1. Many answers possible.

1. 1. 2. [latex]x = \pm 7[/latex]
      3. [latex]x = \pm \sqrt{3}[/latex]
      4. [latex]x = \pm 2i[/latex]
      5. [latex]x = \pm \frac{9}{2}i[/latex]
      6. [latex]x = \pm \sqrt{46}[/latex]
      7. [latex]x = \pm 2\sqrt{7}[/latex]

      ---

1. 1. 8. Up
         Axis of symmetry: [latex]x=0[/latex]
         Vertex:[latex](0,-5)[/latex]
         y-intercept: [latex](0,-5)[/latex]
         x-intercepts: [latex]\left(\pm\frac{\sqrt5}2,0\right)[/latex]
         Domain:[latex]\left(-\infty,\infty\right)[/latex]
         Range: [latex]\lbrack-5,\infty)[/latex]

1. 9. 3.26 seconds
   10. Answers may vary
   11. Many answers possible.

1. 1. 1. [latex]10(y^2 + 1)[/latex]
      2. [latex]3t(t + 2)[/latex]
      3. [latex]3x^2(5 - 7x^3)[/latex]
      4. [latex]6x^4(4 + 5x^3)[/latex]
      5. [latex]6(x^2 - 4x + 5)[/latex]
      6. [latex]2x(4x^2 + 6x - 5)[/latex]
      7. [latex](5x + 2y)(3z + 4)[/latex]
      8. [latex](6x^2 + 5)(4x - 7)[/latex]
      9. [latex]3x(x - 1)(y - 2)[/latex]
      10. [latex](3x - 2)(3y + 10x)[/latex]
      11. [latex]2(4x - 5)(7x + 3y)[/latex]
      12. [latex](4x - 5)(2y + 3)[/latex]

      ---

      13. [latex](x - 2)(x - 4)[/latex]
      14. [latex](x + 1)(x - 15)[/latex]
      15. [latex](x - 4)(x + 7)[/latex]
      16. [latex](x - 3)^2[/latex]
      17. [latex](x + 5)(x - 2)[/latex]
      18. [latex](x - 5)(x + 3)[/latex]
      19. [latex]7(x - 5)(x - 1)[/latex]
      20. [latex]3(x + 4)(x - 2)[/latex]
      21. [latex](2x - 1)(3x + 2)[/latex]
      22. [latex](5x - 4)(x - 2)[/latex]
      23. [latex](3x - 2)(x + 5)[/latex]
      24. Prime
      25. [latex](4x - 3)(2x + 3)[/latex]
      26. [latex](5x + 7)(2x + 1)[/latex]
      27. [latex](x - 2)(3x + 1)[/latex]
      28. [latex](3x - 2)(4x + 3)[/latex]

1. 29. [latex](x + 7)(x - 7)[/latex]
   30. [latex](2x + 9)(2x - 9)[/latex]
   31. Prime
   32. [latex]2x(4x + 1)(4x - 1)[/latex]
   33. [latex]25(x^2 + 4)[/latex]
   34. [latex](7 - x)(7 + x)[/latex]
   35. [latex]x(x + 1)(x - 1)[/latex]
   36. [latex]3x(x + 2)(x - 2)[/latex]

1. 1. 1. [latex]x = \frac{4}{3}, -\frac{4}{3}[/latex]
      2. [latex]x = -7, -1[/latex]
      3. [latex]x = -3, -\frac{1}{2}[/latex]
      4. [latex]x = 3[/latex]
      5. [latex]x = -\frac{5}{2}, 0[/latex]
      6. [latex]t = -3, -6[/latex]
      7. [latex]x = 0, \frac{1}{2}[/latex]
      8. [latex]x = -2, \frac{3}{4}[/latex]
      9. [latex]x = -\frac{1}{5}, -\frac{8}{5}[/latex]
      10. [latex]x = -2, 2[/latex]
      11. [latex]x = 8, -8[/latex]
      12. [latex]t = \frac{7}{4}, -\frac{7}{4}[/latex]
      13. [latex]x = 2, \frac{3}{4}[/latex]
      14. [latex]x = -\frac{5}{3}, -\frac{6}{5}[/latex]
      15. [latex]x = 5, -\frac{7}{2}[/latex]
      16. [latex]t = \frac{3}{2}, -\frac{8}{3}[/latex]
      17. [latex]x = -\frac{3}{2}, \frac{25}{6}[/latex]
      18. [latex]x = \frac{2}{5}, \frac{1}{3}, 0[/latex]
      19. [latex]x = \frac{7}{3}, \frac{4}{3}[/latex]
      20. [latex]x = 0, -\frac{3}{4}, \frac{3}{2}[/latex]
      21. [latex]t = -\frac{1}{3}, \frac{2}{5}[/latex]
      22. [latex]x = -\frac{3}{4}, \frac{2}{3}[/latex]
      23. [latex]x = 3, \frac{2}{7}[/latex]
      24. [latex]x = -4, -\frac{1}{6}[/latex]
      25. [latex]x=-\frac49,\frac49[/latex]
      26. [latex]x = 2, -2[/latex]

      ---

1. 1. 27. Up
          Axis of symmetry:[latex]x=-2[/latex]
          Vertex:[latex](-2,-8)[/latex]
          y-intercept:[latex](0, 0)[/latex]
          x-intercepts:[latex](0, 0),(-4, 0)[/latex]
          Domain: [latex]\left(-\infty\right)[/latex]
          Range: [latex]\lbrack-8,\infty)[/latex]

1. 28. 1. 8 second, 7 seconds
       2. 1
   29. [latex]x=0,-3[/latex]
   30. Explain.

1. 1. 1. [latex]x = -3, -5[/latex]
      2. [latex]t = \pm \frac{5}{2}[/latex]
      3. [latex]x = \frac{5}{3}, -\frac{3}{2}[/latex]
      4. [latex]x = 0, -10[/latex]
      5. [latex]t = -\frac{3}{2}[/latex]
      6. [latex]x = 6, -\frac{1}{4}[/latex]
      7. [latex]x = \frac{4}{3}[/latex]
      8. [latex]x = -\frac{4}{3}, 3[/latex]
      9. [latex]x = 0, -6, 2[/latex]
      10. [latex]x = -\frac{2}{3}, -\frac{4}{3}[/latex]
      11. [latex]x = 0, \frac{1}{5}[/latex]
      12. [latex]t = -3, -\frac{3}{2}[/latex]
      13. [latex]t = 4, \frac{3}{5}[/latex]
      14. [latex]x = 0, \pm \frac{3}{2}[/latex]
      15. [latex]x = -6, \frac{1}{4}, 0[/latex]
      16. [latex]x = -\frac{5}{2}, 1[/latex]
      17. [latex]x = 0, \frac{1}{4}[/latex]
      18. [latex]x = 5, -5[/latex]
      19. [latex]t = \frac{4}{5}, -\frac{2}{3}[/latex]
      20. [latex]x = -\frac{5}{2}, \frac{3}{4}[/latex]
      21. Answers may vary.

      ---

1. 1. 22. Down
          Axis of symmetry: [latex]x=0[/latex]
          Vertex: [latex](0,1)[/latex]
          y-intercept: [latex](0,1)[/latex]
          x-intercepts: [latex](-1,0),(1,0)[/latex]
          Domain: [latex]\left(-\infty,\infty\right)[/latex]
          Range: [latex](-\infty,1\rbrack[/latex]

1. 23. 1. 1 seconds, 3 seconds
       2. 5 seconds
   24. Answers may vary.
   25. Explain.