03.04 LC)
1 answer:
Answer:
y = (x +4)(x +2)²(x +1)
Step-by-step explanation:
The function has a generally U shape, so is of even degree. The zero where the graph touches, but does not cross, the x-axis is a zero of even multiplicity. The minimum degree of a function that matches this description is 4. It will have zeros at x=-4, -2 (multiplicity 2), and -1. The constants in the corresponding binomial factors will be the opposite of these values, so the factored form is ...
y = (x +4)(x +2)²(x +1)
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The multiplicity of a zero is the power of the corresponding factor.
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