## anonymous one year ago Given the function f(x) = -2 |x-5/2|+6 and the graph g(x) shown below, over what interval do the functions f(x) and g(x) have the same minimum value? (Since I cannot graph g(x), its equation is 2|x+0.5| -3 ) @amistre64 @whpalmer4

1. amistre64

what does it mean to have the same minimum value?

2. anonymous

No idea. xD

3. amistre64

well, it can mean 2 things to me ... what are your thoughts?

4. anonymous

I'm assuming it means the smallest value where they intersect

5. amistre64

that was one idea, does f(c) = g(c) ?? this doesnt sit right to me tho. given an interval x = [a,b] f and g have a minimum value within it such that say f(c) = g(d)

6. amistre64

|dw:1443371069792:dw|

7. amistre64

if we have this sort of interval, then we see we have 2 different minimums |dw:1443371139444:dw|

8. amistre64

what are our vertexes?

9. amistre64

and do we have options since there are about an infinite number of intervals we can make that satisfy the results...

10. anonymous

Im lost xd

11. amistre64

what is our vertex of g?

12. anonymous

The answer choices are A [0,8] B [1,7] C [-2,5] D [-5,1] E None of these

13. amistre64

|dw:1443371398297:dw| oh good, choices, then we have something we can compare

14. amistre64

what is our vertex of g, our biggest interval will then be along the y= axis of that vertex

15. anonymous

-.5,3?

16. amistre64

2|x+0.5| -3 ) -0.5, -3 is what it looks like to me, so when does f=-3?

17. anonymous

Not sure

18. amistre64

you have to solve for it ... -2 |x-5/2|+6 = -3 -2 |x-5/2| = -3-6 |x-5/2| = (3+6)/2 etc ...

19. anonymous

Ok so what would that be?

20. amistre64

im not going to do the algebra for you ...

21. anonymous

xd ok bare with my laziness gimme a sec

22. anonymous

x = -2 and x = 7?

23. amistre64

good, so this gives us the largest interval that the minimum of f and g are the same. any option of x < -2 is bad, and any option of x>7 is bad ... can we rule any out?

24. amistre64

outside of -2 to 7, the min of f drops below the min of g .... g cant go lower than its vertex by default

25. anonymous

I can rule D out

26. amistre64

D is bad, and A goes to 8 so it is bad for us too

27. anonymous

So is the answer none of these?

28. amistre64

|dw:1443372355236:dw|

29. amistre64

now, if our interval does NOT include -0.5, then it cannot include -2 or 7 but our only options left have -2 or 7 involved. which one does not contain x=-0.5?

30. anonymous

So it's none of these?

31. amistre64

you havent answered my question ...

32. anonymous

All of them?

33. amistre64

if your not understanding what I am asking for, then say so ...

34. anonymous

Yeah what are you trying to ask?

35. amistre64

im asking for an interval which contains x=-0.5 draw me a number line, -2 to 7 .. and tic off -0.5 for me

36. anonymous

|dw:1443372753726:dw|

37. amistre64

now show me on that drawing, where 1 to 7 fits in ..

38. anonymous

|dw:1443372851792:dw|

39. amistre64

|dw:1443372874804:dw| is -0.5 in the interval from 1 to 7?

40. anonymous

n0pe.

41. amistre64

is -0.5 in the interval from -2 to 5?

42. anonymous

yes

43. amistre64

then we should pick that one.

44. anonymous

So the answer is C?

45. amistre64

i would go with C yes

46. anonymous

Gracias!

47. amistre64