Answer:
.
Step-by-step explanation:
If a graph touches the x-axis at x=c, then (x-c) is a factor of function.
From the given graph it is clear that the graph of function intersect x-axis at x=1 and touch the x-axis at x=-2.
It means (x-1) and (x+2) are not factors of given function but power of (x+2) must be 2.
So, the required function is
...(1)
where, a is a constant.
From the given figure it is clear that the graph passes through the point (-4,-7). So, substitute x=-4 and f(x)=-7 in the above function.
Substitute in (1).
Therefore, the required function is .