## kymber 3 years ago How to find the maximum or minimum value of a quadratic function?

1. 2le

You look at the vertex. Are you at the calculus level or the algebra level?

2. ganeshie8

see the sign of x^2 coeffecient

3. kymber

Algrebra II, year three in high school. It's the same as the vertex?

4. ganeshie8

correct, vertex gives us max/min value. if x^2 coefficient is -ve, its min if x^2 coefficient is +ve, its max

5. ganeshie8

its the opposite actually. if x^2 coefficient is -ve, its max if x^2 coefficient is +ve, its min

6. 2le

What @ganeshie8 said, that will tell you whether the parabola faces up or down. The point at the vertex will be a min or a max depending on that coefficient.

7. ganeshie8

|dw:1349465625929:dw|

8. ganeshie8

so we have minimum value there

9. kymber

So how do you find the value of it?

10. ganeshie8

max/min value = f(-b/2a)

11. ganeshie8

actually it comes from the formula for vertex, vertex = (-b/2a, f(-b/2a))

12. phi

for parabola f(x)= a x^2 + b x +c the x coordinate of the vertex is -b/(2a)

13. kymber

Um, like this? |dw:1349465829395:dw|

14. CliffSedge

Given \[ax^2+bx+c=a(x-h)^2+k\] The vertex is located at (h, k).

15. ganeshie8

|dw:1349465949629:dw|

16. ganeshie8

that gives the x-coordinate only, y-coordinate gives the max/min value.

17. ganeshie8

coordinate is just a number i think

18. kymber

So how do I find the y-coordinate?

19. ganeshie8

since you got, x-coordinate of vertex = -b/2a = 5

20. ganeshie8

put that x value = 5, in the quadratic, it gives u y-coordinate of vertex

21. phi

notice in x^2 -10x +25 b is -10 (negative 10) -b/2a is +10/2*1= 10/2 = +5 use 5 for x in the equation to find the y value

22. kymber

I got it! Thanks guys \(\Large\ddot\smile\)

23. ganeshie8

24. phi

hopefully you got y=0 so the vertex is at (5,0) and the min value is 0

25. ganeshie8

and hw do i get that

26. ganeshie8

smiley..

27. kymber

Yep, I got 0. the smiley is \large\ddot\smile :P

28. ganeshie8

\( \large\ddot\smile \) ah latex is beautifyul :)

29. kymber

Yes it is :D

30. CliffSedge

Thanks, @kymber for teaching us something. \[\large \ddot \smile\] Awesome.

31. kymber

Hehe \(\huge\ddot\smile\)

32. hartnn

yeah , kymber also taught me to draw heart ♥ \(\huge \color{red}{♥}\)

33. CliffSedge

Nice!

34. kymber

\(\Huge\color{pink}{❥}\) Sideways!

35. ganeshie8

i thought only AccessDenied is the latex guru... we have so many experts over here hmm :)

36. ganeshie8

but thats cheating... thats not latex, u using unicode i guess

37. CliffSedge

You're blowing my mind, @kymber !

38. kymber

Lol yeah.. it's not a \(\LaTeX\) command. Just alt codes :|

39. hartnn

still its cool :)

40. kymber

:D

41. ganeshie8

:) yea these things i can see also. but sometime back i tried to use crossed swords unicode, and it didnt show up in many browsers :( from then i stopped using unicode, not sure why only few unicode characters show up...

42. ganeshie8

this one : http://www.fileformat.info/info/unicode/char/2694/index.htm see if u can get this here...

43. kymber

\(\Huge{⚔}\)

44. kymber

Lol.

45. ganeshie8

i see a box, what u see at ur end hmm

46. kymber

:| I see the swords..

47. hartnn

i see box also

48. kymber

What browser are you guys using?

49. hartnn

chrome O.o

50. ganeshie8

chrome too

51. kymber

I'm using Mozilla :P

52. ganeshie8

firefox ?

53. hartnn

54. kymber

Yeah. I switched to Chrome and it's a box. Use Mozilla! :P

55. ganeshie8

mozilla wins !

56. hartnn

what kind of black magic is this!

57. CliffSedge

Firefox is simply superior . .