anonymous
  • anonymous
Find the vertex of the graph of the function. f(x) = 4x2 + 24x + 32
Mathematics
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anonymous
  • anonymous
Find the vertex of the graph of the function. f(x) = 4x2 + 24x + 32
Mathematics
chestercat
  • chestercat
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FireKat97
  • FireKat97
the vertex lines on the axes of symmetry for a parabola, so first you want to find that and you can do so by using axes of symmetry = -b/2a where y = ax^2 + bx + c
FireKat97
  • FireKat97
lies*
anonymous
  • anonymous
f(x) = 4x2 + 24x + 32 b=24 a=4 -b/2a -24/8

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FireKat97
  • FireKat97
yup thats correct! so now to find the y coordinate that goes with this, we simply sub -24/8 = -3, into the equation, to solve for y
anonymous
  • anonymous
Hmm how did you get the -3 ? Sorry I'm really bad at math !!
FireKat97
  • FireKat97
Oh thats okay! I just simplified -24/3 because 3 goes into 24, 8 times and we have a minus out the front as well... @ashhhrodriguez
anonymous
  • anonymous
Oh WOW thank you! What exactly do I sub 3 for all the x values ?
anonymous
  • anonymous
I mean -3!
FireKat97
  • FireKat97
okay so we know that at our axes of symmetry, x = -3, right?
FireKat97
  • FireKat97
Now we want to sub this back into the equation, to find out what y is equal to as x = -3... agreed?
anonymous
  • anonymous
Ohh so we already have our x value to our vertex -3
FireKat97
  • FireKat97
yuppp thats what the equation -b/2a gave us
FireKat97
  • FireKat97
so now we have to find the y value which goes with it
FireKat97
  • FireKat97
and we can do that by subbing x = -3 back into the original equation
anonymous
  • anonymous
(-3,-4) Thank you so so much !
FireKat97
  • FireKat97
Yup thats correct! And no problem! :)

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