How to know when estimated coefficients of a quadratic function are zero by looking at graph?

Question

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!

Answer 1

• $w_0=0$ 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!

Answer 2

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