Predict the relationship between the graph of y=x^3 - x^2 and the graph of y+3=(x - 2)^3 - (x - 2)^2. graph each function. - , i’m honestly very lost. i’ve attached a photo to you see the question better too.

Remark

If you start with the graph y = x^3 - x^2, it will cross the x axis at (0,0).  The y intercept for that graph is when x = 0. Thus  y = 0^3 - 0^2 = 0 when x = 0 and that 's how you derive (0,0)

Remark 2

Now watch that point (0,0) on the left graph below when you change it to y = (x - 2)^3 - (x - 2)^2 [Never mind the 3 for now. We'll deal with it later on]. Notice that what is happening at (2,0) is what is happening with the blue graph as compared to the red one. The change is very dramatic. Instead of going up, both graphs start to go down at the points I'm telling you to watch.

Conclusion 1.

So the first prediction you should make is that the - 2 forces the graph to move 2 units to the right.

Remark 3

What about the three on the right hand side? It is easier if you rewrite the equation as y = (x-2)^3 - (x -2)^ - 3. That means you have subtracted three from the right side. That should move (2,0) down 3 units. (minus is down when a number is on the right.)  The green line in the right graph shows you that.

Conclusion 2

The green line shows you the final movement. (0,0) goes 3 units down and 2 units right. The new point we have been watching is (2,3)

answer: #1 ads up by 8 and i don't know #2

6. 104

7. 52/37

8. 2704

9. 140608

10. -52

11. |52|=52

12. 1/52

13. 156

14. 26

15. 40

16. 37

17. -364

18. 53 1/3

19. 50.96

20. 43 2/3

21. 78

22. 50.75

23. 47.63

24. 163.28

25. 10400

26. 338

27. 208

28. 2704 square inches

29. 312 square meters

30. don't know what its asking, tell me so i can tell you

31. 8490.56

32. 52 degrees would be an acute angle

33. 128 degrees

34. 20.8

35. 39

36. 208