Answer:
f(x) = 1/8(x +4)^2(x +1)(x -3)
Step-by-step explanation:
The end behavior shows both ends of the graph headed to +∞. That means ...
- the function is of even degree
- the leading coefficient is positive
There are zeros at x=-4, -1, 3. The graph does not cross the x-axis at x=-4, so that zero has even degree. The smallest degree that will satisfy the degree requirements is 4, where the zero at x=-4 is of multiplicity 2.
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You know that zero x=p means (x-p) is a factor. The multiplicity is the exponent of the factor, so the factored function so far is ...
f(x) = (1/a)(x +4)^2(x +1)(x -3)
When x=0, this is ...
f(0) = 1/a(4^2)(1)(-3) = -48/a
The graph shows you the y-intercept is -6, so ...
-6 = -48/a
a = 8
The factored polynomial is ...
[tex]f(x)=\dfrac{1}{8}(x+4)^2(x+1)(x-3)[/tex]
