## iwanttogotostanford one year ago HELP PLEASE IM STUCK: Using the completing-the-square method, find the vertex of the function f(x) = –2x^2 + 12x + 5 and indicate whether it is a minimum or a maximum and at what point. Maximum at (–3, 5) Minimum at (–3, 5)

1. jim_thompson5910

Vertex form is $$\Large y = a(x-h)^2+k$$ The vertex of that equation is $$\Large (h,k)$$ From $$\Large -2x^2 + 12x + 5$$ we see that $$\Large a = -2, b = 12, c = 5$$ Plug the values of 'a' and 'b' into the formula $\Large h = \frac{-b}{2a}$ to find the value of h. Tell me what you get

2. anonymous

3. iwanttogotostanford

so it would be A? @jim_thompson5910

4. jim_thompson5910

why maximum?

5. iwanttogotostanford

because it increases

6. jim_thompson5910

you're looking at the graph I'm guessing?

7. iwanttogotostanford

yes

8. jim_thompson5910

do you know how to determine without the graph? by just looking at the value of 'a'

9. iwanttogotostanford

no, but can you just determine by looking at the graph?

10. jim_thompson5910

well let's say we don't have a graphing calculator since 'a' is a negative number, this means that the parabola opens downward like this |dw:1442446419996:dw| a good way to remember this is to think "The value of 'a' is negative. Negative means sad, so we have a sad face graph"

11. iwanttogotostanford

ok

12. jim_thompson5910

and of course, at the peak of this "sad face graph" is the vertex. Which in this case, is the max |dw:1442446478716:dw|

13. jim_thompson5910

do you know how to find h and k without graphing?

14. iwanttogotostanford

no

15. jim_thompson5910

use the formula I posted earlier use h = -b/(2a)

16. jim_thompson5910

plug in a = -2 and b = 12 into that formula what is the value of h?

17. iwanttogotostanford

the value of H would be -3 right?

18. jim_thompson5910

yes, let's do another example Let's say we had y = 3x^2-30x+85 what are the values of a,b,c ? what is the value of h?

19. iwanttogotostanford

a=3x^2 b=-30 c=85 and then h would be 30/18? i think i got it wrong...

20. jim_thompson5910

a,b,c are just numbers (no variables attached)

21. jim_thompson5910

a = 3, b = -30, c = 85

22. jim_thompson5910

To find h, we do this $\Large h = \frac{-b}{2a}$ $\Large h = \frac{-(-30)}{2*3}$ $\Large h = ???$

23. iwanttogotostanford

can you give me one second? please just one minute:-)

24. jim_thompson5910

Take all the time you need. There's no rush.

25. iwanttogotostanford

ok, so i worked it out and found that it was B

26. jim_thompson5910