iwanttogotostanford
  • iwanttogotostanford
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)
Mathematics
  • Stacey Warren - Expert brainly.com
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SOLVED
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katieb
  • katieb
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jim_thompson5910
  • 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
anonymous
  • anonymous
Oh, I thought you already know the answer to this. Hmmm.
iwanttogotostanford
  • iwanttogotostanford
so it would be A? @jim_thompson5910

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jim_thompson5910
  • jim_thompson5910
why maximum?
iwanttogotostanford
  • iwanttogotostanford
because it increases
jim_thompson5910
  • jim_thompson5910
you're looking at the graph I'm guessing?
iwanttogotostanford
  • iwanttogotostanford
yes
jim_thompson5910
  • jim_thompson5910
do you know how to determine without the graph? by just looking at the value of 'a'
iwanttogotostanford
  • iwanttogotostanford
no, but can you just determine by looking at the graph?
jim_thompson5910
  • 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"
iwanttogotostanford
  • iwanttogotostanford
ok
jim_thompson5910
  • 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|
jim_thompson5910
  • jim_thompson5910
do you know how to find h and k without graphing?
iwanttogotostanford
  • iwanttogotostanford
no
jim_thompson5910
  • jim_thompson5910
use the formula I posted earlier use h = -b/(2a)
jim_thompson5910
  • jim_thompson5910
plug in a = -2 and b = 12 into that formula what is the value of h?
iwanttogotostanford
  • iwanttogotostanford
the value of H would be -3 right?
jim_thompson5910
  • 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?
iwanttogotostanford
  • iwanttogotostanford
a=3x^2 b=-30 c=85 and then h would be 30/18? i think i got it wrong...
jim_thompson5910
  • jim_thompson5910
a,b,c are just numbers (no variables attached)
jim_thompson5910
  • jim_thompson5910
a = 3, b = -30, c = 85
jim_thompson5910
  • jim_thompson5910
To find h, we do this \[\Large h = \frac{-b}{2a}\] \[\Large h = \frac{-(-30)}{2*3}\] \[\Large h = ???\]
iwanttogotostanford
  • iwanttogotostanford
can you give me one second? please just one minute:-)
jim_thompson5910
  • jim_thompson5910
Take all the time you need. There's no rush.
iwanttogotostanford
  • iwanttogotostanford
ok, so i worked it out and found that it was B
jim_thompson5910
  • jim_thompson5910
I'm asking for a number
jim_thompson5910
  • jim_thompson5910
if you plug a = 3 and b = -30 into that h formula, what result do you get?

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