1.

1. Opens up

2. Vertex: (1, 2)

3. Axis: $x=1$

4. No x-intercept

5. y-intercept: 3

6. Decreasing on $(-\infty ,1),$ increasing on $(1,\infty )$

3.

1. Opens down

2. Vertex: (3, 4)

3. Axis: $x=3$

4. x-intercepts: $3\pm \sqrt{2}$

5. y-intercept: $-14$

6. Increasing on $(-\infty ,3),$ decreasing on $(3,\infty )$

5.

1. Opens down

2. Vertex: (0, 3)

3. Axis: y-axis

4. x-intercepts: $\pm {\displaystyle \frac{\sqrt{6}}{2}}$

5. y-intercept: 3

6. Increasing on $(-\infty ,0),$ decreasing on $(0,\infty )$

7.

1. Opens up

2. Vertex: (1, 1)

3. Axis: $x=1$

4. No x-intercept

5. y-intercept: 3

6. Decreasing on $(-\infty ,1),$ increasing on $(1,\infty )$

9.

1. Opens up

2. Vertex: $\left({\displaystyle \frac{1}{3}},{\displaystyle \frac{2}{3}}\right)$

3. Axis: $x={\displaystyle \frac{1}{3}}$

4. No x-intercept

5. y-intercept: 1

6. Decreasing on $\left(-\infty ,{\displaystyle \frac{1}{3}}\right),$ increasing on $\left({\displaystyle \frac{1}{3}},\infty \right)$

11. Minimum: $-1$

13. Maximum: ${\displaystyle \frac{25}{8}}$

15. Shift the graph of $y=x^3$ one unit to the left and two units down.

17. Shift the graph of $y=x^3$ one unit right, reflect the resulting graph in the x-axis, and shift it one unit up.

19.

1. $f(x)\to -\infty$ as $x\to -\infty$ and $f(x)\to \infty$ as $x\to \infty$

2. Zeros: $x=-2,$ multiplicity: 1, the graph crosses the x-axis; $x=0,$ multiplicity: 1, the graph crosses the x-axis; $x=1,$ multiplicity: 1, the graph crosses the x-axis.

3. x-intercepts: $-2,$ 0, 1; y-intercept: 0

4. The graph is above the x-axis on $(-2,0)\cup (1,\infty )$ and below the x-axis on $(-\infty ,-2)\cup (0,1).$

5. Symmetry: none

6. 

21.

1. $f(x)\to -\infty$ as $x\to -\infty$ and $f(x)\to -\infty$ as $x\to \infty$

2. Zeros: $x=0,$ multiplicity: 2, the graph touches but does not cross the x-axis; $x=1,$ multiplicity: 2, the graph touches but does not cross the x-axis.

3. x-intercepts: 0, 1; y-intercept: 0

4. The graph is below the x-axis on $(-\infty ,0)\cup (0,1)\cup (1,\infty ).$

5. Symmetry: none

6. 

23.

1. $f(x)\to -\infty$ as $x\to -\infty$ and $f(x)\to -\infty$ as $x\to \infty$

2. Zeros: $x=-1$, multiplicity: 1, the graph crosses the x-axis; $x=0$, multiplicity: 2, the graph touches but does not cross the x-axis; $x=1$ multiplicity: 1, the graph crosses the x-axis.

3. x-intercepts: $-1,$ 0, 1; y-intercept: 0

4. The graph is above the x-axis on $(-1,0)\cup (0,1)$ and below the x-axis on $(-\infty ,-1)\cup (1,\infty ).$

5. The graph is symmetric with respect to the y-axis.

6. 

25. Quotient: $2x+3;$ remainder: $-7$

27. Quotient: $8x^3-12x^2+14x-21;$ remainder: 186

29. Quotient: $x^2+3x-3;$ remainder: $-6$

31. Quotient: $2x^3-5x^2+10x-17;$ remainder: 182

33. $-11$

35. 88

37. 1, 2, 4

39. $-3,-2,{\displaystyle \frac{1}{3}}$

41. $-6,-3,-2,-1,1,2,3,6$

43. $-2,-{\displaystyle \frac{1}{5}},0$

45. $-3,-2,2$

47. $-2,3\pm \sqrt{2}$

49. ${\displaystyle \frac{1}{2}},1\pm \sqrt{3}$

51. $-3,1,2$

53. $-1,3,3i,-3i$

55. $2i,-2i,-1+2i,-1-2i$

57. $\{-2,1,2\}$

59. $\left\{-1,-{\displaystyle \frac{1}{2}},{\displaystyle \frac{3}{2}}\right\}$

61. $\{2,3\pm i\sqrt{2}\}$

63. $\left\{-{\displaystyle \frac{1}{3}},1\pm i\sqrt{5}\right\}$

65. $\{-1,2,i,-i\}$

67. $\left\{-2,{\displaystyle \frac{1}{2}},1\pm i\sqrt{2}\right\}$

69. The only possible rational roots are $-2,-1,1,$ and 2. None of them satisfy the equation.

71. 1.88

73. x-intercept: $-1;$ no y-intercept; vertical asymptote: y-axis; horizontal asymptote: $y=1;$ symmetry: none. The graph is above the x-axis on $(-\infty ,-1)\cup (0,\infty )$ and below the x-axis on $(-1,0).$

75. x-intercept: 0; y-intercept: 0; vertical asymptotes: $x=-1$ and $x=1;$ horizontal asymptote: x-axis. The graph is above the x-axis on $(-1,0)\cup (1,\infty )$ and below the x-axis on $(-\infty ,-1)\cup (0,1).$

77. x-intercept: 0; y-intercept: 0; vertical asymptotes: $x=-3$ and $x=3;$ no horizontal asymptote. The graph is above the x-axis on $(-3,0)\cup (3,\infty )$ and below the x-axis on $(-\infty ,-3)\cup (0,3).$

79. x-intercept: 0; y-intercept: 0; vertical asymptotes: $x=-2$ and $x=2;$ no horizontal asymptote. The graph is above the x-axis on $(-\infty ,-2)\cup (2,\infty )$ and below the x-axis on $(-2,0)\cup (0,2).$