For the following exercises, use the given information about the polynomial graph to write the equation. Zeros at x = −2, x = 1, and x = 3. (0, −4).

postillan4 2021-09-30 Answered
For the following exercises, use the given information about the polynomial graph to write the equation. Degree 3. Zeros at x = −2, x = 1, and x = 3. y-intercept at (0, −4).

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Expert Answer

Ezra Herbert
Answered 2021-10-01 Author has 17613 answers
Data: x — intercept=-2,1,3
© — intercept of multiplicity =-4
Degree=4
Since it is a third degree function with three x intercepts, its general equation becomes: \(\displaystyle{f{{\left({x}\right)}}}={a}{\left({x}+{2}\right)}{\left({x}—{1}\right)}{\left({x}-{3}\right)}\)
In order to evaluate a, use the y - intercept (0,-4), therefore substitute f(0)=-4 in this equation:
\(\displaystyle-{4}={a}{\left({0}+{2}\right)}{\left({0}—{1}\right)}{\left({0}-{3}\right)}\)
Simplify: -4=6a
Evaluate a: \(\displaystyle{a}=-\frac{{4}}{{6}}=-{\left(\frac{{2}}{{3}}\right)}\)
This implies that the equation of the given polynomial function is f(x) =
\(\displaystyle{\left(-{\left(\frac{{2}}{{3}}\right)}\right)}{\left({x}+{3}\right)}{)}{\left({x}—{1}\right)}{\left({x}-{3}\right)}\)
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