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Construct a polynomial function with the stated properties. Reduce all fractions to lowest terms.
Construct a polynomial function with the stated properties. Reduce all fractions to lowest terms.Third-degree, with zeros of −2,−1, and 3, and passes through the point (1,12)
Step 1: Convert zeros to factors of the polynomial.The allows us to convert zeros of -2, -1, and 3 into the factors (x+2)(x+1)(x-3).This gives us the foundation of the polynomial, but it's missing a key piece, the leading coefficient which causes the vertical stretch/compression to hit the desired point.So right now we have y = a · (x+2)(x+1)(x-3)Step 2: Find "a".This is where the point (1,12) comes in. We need to substitute x=1 and y=12 into the equation above to find a.12 = a · (1+2)(1+1)(1-3)12 = a · (3)(2)(-2)12 = a · (-12)-1 = aThat's the full function:f(x) = -1 (x+2)(x+1)(x-3)...
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