## anonymous one year ago I need help on a assignment!

1. anonymous

1. West Mathington’s most urgent need is a parabolic freeway. Create your own upward opening quadratic function, f(x), which has two real zeros. Prove that f(x) has two real zeros. 2. Two on-ramps need to be placed on the parabolic freeway. Decide where on the parabola of f(x) you are placing the on-ramp locations. Write those ordered pairs down. 3.West Mathington wants to connect these on-ramps with some surface roads. Create a linear growth function, h(x), that passes through both on-ramp points. Create an exponential growth function, j(x), that passes through at least one of the on-ramp points. Show all of the work you did to create both functions. I did those but I need help on the rest!

2. anonymous

I need help on 4 and 5

3. anonymous

4. What important relationship do the x-coordinates of the on-ramp location points have with the system of equations formed by the two roads’ functions that are being connected? Provide justification and support for your explanation. 5. The city planner needs to identify the most northern road. Prove which road will eventually go the furthest to the north (positive y-direction). Create tables for your functions using an appropriate domain of five integers. Using the tables and graph, explain to the city planner which road will be the furthest north as the x-values continue to get larger (the road continues to go east). Provide reasoning why.

4. anonymous

@triciaal

5. triciaal

2 real zeros when b^2 = 4 a c from the general equation ax^2 + bx + c = 0

6. anonymous

wait how would i explain it for number 4?

7. triciaal

upward opening means a is positive

8. anonymous

I did 1-3. I just need some help on 4 and 5

9. triciaal

show what you have then

10. anonymous

ok hang on one sec

11. triciaal

@peachpi @sleepyjess @Data_LG2

12. anonymous

1. f(x) = x^2 - 1 2. I got the points (-1,0) and (2,3) 3. linear function: y=x+1 exponential function: f(x) = 2^x -1

13. triciaal

14. anonymous

@triciaal where are you going??

15. anonymous

@sleepyjess @Michele_Laino

16. Michele_Laino

17. anonymous

thanks! umm im just confused about 4 and 5 though can you help? @Michele_Laino

18. Michele_Laino

I think that we have to write the function of each on-ramp

19. anonymous

ok would i say that the important relationship the x-coordinates of the on-ramp location points have with the system of equations is that the freeway and roads become connected? I would provide justification and support for your explanation by showing the graph and label everything? for number 4

20. anonymous

@Michele_Laino

21. Michele_Laino

yes! I think so!

22. anonymous

ok thanks! what about number 5??

23. anonymous

how would i make the tables?

24. Michele_Laino

for part #5, we have to construct those two on-ramps

25. anonymous

how would i do that

26. Michele_Laino

one on-ramp has to pass at point (-1,0), and the other one has to pass at point (2,3). Furthermore both on-ramp have to be represented by a straight line, so the corresponding function has to be like this: y= a*x+b

27. anonymous

wait i already did that? number 5 wants a table how do i do that?

28. Michele_Laino

I think that one on-ramp can be represented by this function: $y = \frac{1}{2}\left( {x + 1} \right)$

29. anonymous

i'm confused now?

30. Michele_Laino

and the second one, can be represented by this function: $y = - x + 5$

31. anonymous

for number 5? arent they asking for a table though

32. Michele_Laino

I know, nevertheless in order to write a table, you have to start with a function

33. Michele_Laino

as you can check, the first function: y=(1/2)(x+1) passes at point (-1,0)

34. anonymous

ok so i would make a table for each function 1. f(x) = x^2 - 1 2. y = x + 1 3. f(x) = 2^x -1

35. Michele_Laino

whereas the second function: y=-x+5, passes at point (2,3)

36. anonymous

ok so I would start with the first point each function passes through to the fifth point they pass?

37. Michele_Laino

yes! It is a possible procedure

38. anonymous

ok so thats all I would do then explain? thanks so much!

39. Michele_Laino

:)