anonymous
  • anonymous
Given the functions f(x) = 3x2, g(x) = x2 − 4x + 5, and h(x) = –2x2 + 4x + 1, rank them from least to greatest based on their axis of symmetry.
Mathematics
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schrodinger
  • schrodinger
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welshfella
  • welshfella
f(x) = 3 x^2 when x = 0 f(x) = 0 so what is the axis of symmetry of this function?
anonymous
  • anonymous
f(x)=0
welshfella
  • welshfella
no its x = 0 - in other words its the f(x) ( or y axis) |dw:1434834269396:dw|

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anonymous
  • anonymous
-1/6
welshfella
  • welshfella
?? - what is -1/6??
anonymous
  • anonymous
f(x) axis of symmetry
welshfella
  • welshfella
you've lost me!! axis of symmetry for which function?
welshfella
  • welshfella
the axis of symmetry is a vertical line for these functions and is x = something
welshfella
  • welshfella
|dw:1434834621668:dw|
welshfella
  • welshfella
the axis of symmetry is the vertical line cutting the curve in 2.
anonymous
  • anonymous
ok shouldn't I use -b/2a to find it??
welshfella
  • welshfella
yes - but in the case of 3x^2 you needn't use it but you can - note that b = 0 in this case so -b/2a = 0/6 = 0
welshfella
  • welshfella
so its x = 0
anonymous
  • anonymous
Ok. So what about g(x)?
anonymous
  • anonymous
would that one be 2?
welshfella
  • welshfella
-b / 2a = -(-4) / 2 = 4/2 = 2 yes
welshfella
  • welshfella
for h(x) its -4 / 2* -2 = -4 / -4 = 1
welshfella
  • welshfella
least to greatest is f(x) , h(x), g(x) 0,1,2
welshfella
  • welshfella
ok
anonymous
  • anonymous
Given the function f(x) = x2 and k = 2, which of the following represents a horizontal shift? f(x) + k kf(x) f(x + k) f(kx)
anonymous
  • anonymous
@welshfella
welshfella
  • welshfella
without giving you a direct answer here is an example if we have f(x) = x^2, f(x+1)^2 will shift the graph horizontally 1 unit to the left
welshfella
  • welshfella
* that is f(x + 1) = (x + 1)^2

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