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:


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!

  • $w_0=0$ 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!


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

  • 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

Your Answer

By clicking “Post Your Answer”, you agree to our terms of service, privacy policy and cookie policy

Not the answer you're looking for? Browse other questions tagged or ask your own question.