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I have a quadratic function:

$f(x) = w_0 + w_1 \cdot x + w_2 \cdot (x^2)$

How would I know which estimated coefficients are zero by look at a graph? For example:

graphs

I can clearly see that the line starts on y=0 on the above first and thrid graphs. And that both x and y of the line start at 0 for the second and fourth graphs.

But, how would I know which estimated coefficients are zero for each graph?

Disclaimer: I never took linear algebra. Any explanation or even links would be appreciated! Thanks!

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  • $w_0=0$ if and only if the graph starts from the origin $(0,0)$ (true for every polynomials of any degree);
  • $w_2=0$ if and only if the graph is a straight line (true of for polynomials of degree 2);
  • $w_1=0$ if and only if the axis parabola is exactly the y-axis or the graph is an horizontal line (degree-2 polynomials).

Remember that you cannot always see this at first blush!

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1st Image : $w_2=0$,

2nd Image : $w_0=0$, $w_2=0$

3rd Image : None of $w_0,w_1,w_2$ are zero

4th Image : $w_0$=0

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  • 2
    $\begingroup$ Your Readers will have difficulty deciphering how you got these answers, and the Question asks "how to know". $\endgroup$ – hardmath Mar 24 '16 at 12:06

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