Quadratic Functions

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]

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

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

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

15. 1. Yes
    2. No

16. Infinity and negative infinity; Discuss with classmates.

1. 1
2. none
3. 1

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. Upaxis of symmetry: [latex]x=3[/latex]

   vertex: [latex](3,4)[/latex]

   y-intercept: [latex](0,13)[/latex]

   x-intercepts: none

   Domain : [latex]\left(-\infty,\infty\right)[/latex]

   Range: [latex]\lbrack4,\infty)[/latex]

5. Downaxis of symmetry: [latex]x=-1[/latex]

   vertex: [latex](-1,0)[/latex]

   y-intercept: [latex](0,-1)[/latex]

   x-intercepts: 1

   Domain : [latex]\left(-\infty,\infty\right)[/latex]

   Range: [latex](-\infty,0\rbrack[/latex]

6. Downaxis of symmetry: [latex]x=2[/latex]

   vertex: [latex](2,7)[/latex]

   y-intercept: [latex](0,3)[/latex]

   x-intercepts: 2

   Domain : [latex]\left(-\infty,\infty\right)[/latex]

   Range: [latex](-\infty,7\rbrack[/latex]

7. Downaxis of symmetry: [latex]x=-5[/latex]

   vertex: [latex](-5,-7)[/latex]

   y-intercept: [latex](0,-82)[/latex]

   x-intercepts: none

   Domain : [latex]\left(-\infty,\infty\right)[/latex]

   Range: [latex](-\infty,-7\rbrack[/latex]

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?
2. 1. feet per second
   2. height above the ground
   3. feet
   4. time
   5. seconds
   6. the graph is a parabola opening down.

3. 1. seconds
   2. meters
   3. seconds
4. 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. 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]

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. [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.

18. axis of symmetry: [latex]x=1[/latex]; (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]

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]

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.

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]

19. 1.57 seconds
20. 1.45 seconds
21. [latex]\approx10.32[/latex] seconds longer
22. 1. 2 seconds
    2. 382 feet
    3. Domain [latex]=[0,4.763][/latex]; Range [latex]=[0,382][/latex]
    4. 

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.

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]

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]

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

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]

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. [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]

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

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

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.

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]

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