## Empty one year ago 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:

1. Empty

$\left[ \begin{array}c 0 & 0 & 0\\1/4 & 1/2 & 1\\1 & 1 & 1\\\end{array} \right]\left[ \begin{array}c a\\ b\\ c\\\end{array} \right] =\left[ \begin{array}c 0\\ 1\\ 0\\\end{array} \right]$ I can't invert this matrix!

2. anonymous

i can't make head or tails of what that is supposed to do

3. Empty

Waittt.t.... I just realized my problem

4. Empty

I put a full 0 vector in that top column, the last one should be a 1.

5. anonymous

this is way way too much work to solve this very easy question, right?

6. Empty

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.