Answer: [tex]f(x)=-(x-5)^{2}(x+2)[/tex]
Step-by-step explanation:
There is a double root at x=5 and a single root at x=-2, so we know f(x) is of the form [tex]f(x)=a(x-5)^{2}(x+2)[/tex] for some constant a.
To find a, we can substitute the coordinates of the y-intercept, (0, -50).
[tex]-50=a(0-5)^{2}(0+2)\\\\-50=50a\\\\a=-1[/tex]
So, [tex]f(x)=-(x-5)^{2}(x+2)[/tex]
