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Examine the function $y = x^2 - 4x + 3$ and determine:

  • if the curve has a maximum or minimum point?
  • the function's zeroes
  • the function's line of symmetry,
  • coordinates of the turning point
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Have you calculus techniques at hand? – David Mitra Apr 1 '12 at 21:39
Have you tried completing the square? – Michael Joyce Apr 1 '12 at 21:52
Note that you can easily factor the function into $(x-3)$ $(x-1)$. Your zeroes should be obvious from that. And, I second David Mitra's comment. Some derivatives would make this process for extrema slightly easier. – Joe Apr 1 '12 at 21:54
Can you graph it? – Neal Apr 1 '12 at 21:54
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To answer all your questions, try to complete the square so that the function is written in the form $$y = a(x-b)^2 + c.$$ In this form, it is easy to determine whether the function has a maximum or a minimum (this will depend on the value of $a$), the zeros (this will depend on $a$, $b$, and $c$), the line of symmetry (depends on $b$), and the turning point (again, depends on $b$).

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