anonymous
  • anonymous
Using the completing-the-square method, find the vertex of the function f(x) = 2x2 − 8x + 6 and indicate whether it is a minimum or a maximum and at what point. Maximum at (2, –2) Minimum at (2, –2) Maximum at (2, 6) Minimum at (2, 6)
Mathematics
  • Stacey Warren - Expert brainly.com
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SOLVED
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schrodinger
  • schrodinger
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Mehek14
  • Mehek14
since the first term is positive = \(2x^2\) that means it is opening upwards so the vertex would be the minimum that eliminates A and C
Mehek14
  • Mehek14
to find the vertex, use \(\dfrac{-b}{2a}\) in your equation, you have b = -8 a = 2 \(\dfrac{-(-8)}{2*2}=\dfrac{8}{4}=2\) so x = 2
Mehek14
  • Mehek14
plug x = 2 into the equation

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Mehek14
  • Mehek14
@boots_2000 can you do that?
anonymous
  • anonymous
Yeah so is it maximum 2,6?
anonymous
  • anonymous
@Mehek14
IrishBoy123
  • IrishBoy123
it says "Using the completing-the-square method"
Mehek14
  • Mehek14
no did you plug in x = 2 in the equation
anonymous
  • anonymous
yeah
welshfella
  • welshfella
using completing the square:- = 2(x^2 - 4x + 3) = 2[(x - 2)^2 - c + 3] can you tell me the value of c - can you remember from the last post?
Mehek14
  • Mehek14
\(f(2)=2*2^2-8*2+6\\2^2=4\\2*4=8\\8*2=16\\8-16=-8\) add \(-8+6\)
IrishBoy123
  • IrishBoy123
+1 @welshfella
anonymous
  • anonymous
so its minimum? lol
Mehek14
  • Mehek14
\(\color{#0cbb34}{\text{Originally Posted by}}\) @Mehek14 since the first term is positive = \(2x^2\) that means it is opening upwards so the vertex would be the minimum that eliminates A and C \(\color{#0cbb34}{\text{End of Quote}}\)
welshfella
  • welshfella
its a minimum but what are the coordinates at the minimum?
anonymous
  • anonymous
2,6
Mehek14
  • Mehek14
\(\color{#0cbb34}{\text{Originally Posted by}}\) @Mehek14 \(f(2)=2*2^2-8*2+6\\2^2=4\\2*4=8\\8*2=16\\8-16=-8\) add \(-8+6\) \(\color{#0cbb34}{\text{End of Quote}}\)
welshfella
  • welshfella
No mehek has worked the y coordinate for you you can also get from the completing the square method
anonymous
  • anonymous
so 2,-2
Mehek14
  • Mehek14
yes
anonymous
  • anonymous
could you guys come and help me quick when you're all done here?
welshfella
  • welshfella
I'll carry from where i left off 2[(x - 2)^2 - c + 3] c = 4 because -2^2 = + 4 = 2(x - 2)^2 - 1) = 2(x - 2)^2 - 2 so the vertex is at ( 2,-2) you get this by comparing your expression with the genarl form for the vertex
anonymous
  • anonymous
please
welshfella
  • welshfella
|dw:1440256991772:dw|

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