Question

-2(x-3)^3(x-3)^2(x+1) find both the x and y intercepts. I have found the x intercepts: -1,2,3 but am struggling to find the y intercepts.

Answer 1

$\bf -2(x-3)^3(x-3)^2(x+1)=0\impliedby x-intercepts \\\\\\ x= \begin{cases} 3\\ -1 \end{cases}$

now, the (x-3) is there 5 times,  namely (x-3)(x-3)(x-3) and (x-3)(x-3), that simply means, the root of 3 has a multiplicity of 5, is all

to get the y-intercepts, simple, when the graph touches the y-axis, "x" is zero, thus $\bf -2(0-3)^3(0-3)^2(0+1)=y\impliedby y-intercepts \\\\\\ -2(-3)^3(-3)^2(1)=y\implies -2(-27)(9)(1)=y\implies 486=y$