<s>[INST] Finding $a, b, c$ values of a polynomial from a graph. I was doing my homework and I am now stuck on question number 7 which is:
The diagram shows the curve with the equation $y = (x + a)(x - b)^2$ where $a$ and $b$ are positive integers.
(i) Write down the values of $a$ and $b$, and also of $c$, given that the curve crosses the $y$-axis at $(0, c)$.
I have attached a picture of my text book here:

I have so far found $b$ like this:
$(x - b)^2 = x^2 - 2bx + b^2$
Since $y = 0$ at $x = 1$,
$0 = 1 - 2b + b^2$
Solving that quadratic equation gives us  $b = 1$. 
I need to find $a$ and $c$ and I am totally puzzled on how to find them.
 [/INST] From the graph it is evident that the roots are $-2$ and $1$ ($1$ being a repeated root), 
So the equation becomes: 
$$(x+2)(x-1)^2=0$$
Comparing it with $$(x+a)(x-b)^2=0$$ We find $a=2,b=1$
Also for finding the point $(0,c)$ we can plug in $x=0$ in the equation $y=(x+2)(x-1)^2$ and we get $c=2$
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