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.