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We can define a certain parabola by saying it goes through the points (0,0), (1/2,1), (1,0). I know the answer to this. However I don't understand why this method fails:
Mathematics
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We can define a certain parabola by saying it goes through the points (0,0), (1/2,1), (1,0). I know the answer to this. However I don't understand why this method fails:
Mathematics
chestercat
  • chestercat
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\[\left[ \begin{array}c 0 & 0 & 0\\1/4 & 1/2 & 1\\1 & 1 & 1\\\end{array} \right]\left[ \begin{array}c a\\ b\\ c\\\end{array} \right] =\left[ \begin{array}c 0\\ 1\\ 0\\\end{array} \right]\] I can't invert this matrix!
anonymous
  • anonymous
i can't make head or tails of what that is supposed to do
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Waittt.t.... I just realized my problem

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I put a full 0 vector in that top column, the last one should be a 1.
anonymous
  • anonymous
this is way way too much work to solve this very easy question, right?
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Ahhh so it just represents the system of equations from plugging in the points to: \(ax^2+bx+c = f(x) \) Yeah you're right the best way I found to do this is we are given two roots so we write: f(x) = k(x-0)(x-1) and plug in the point f(1/2)=1 to solve for k.

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