Question

Construct a polynomial function with the stated properties. Reduce all fractions to lowest terms.

Second-degree, with zeros of −4 and 6, and goes to −∞ as x→−∞.


p(x) =

Answer 1

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Answer:

p(x) = -x^2 +2x +24

Explanation:

When the polynomial has a zero at x=q, it has a factor of (x -q). The zeros of -4 and 6 tell you the factors are (x -(-4)) and (x -6). The end behavior tells you the leading coefficient is negative.

p(x) = -(x +4)(x -6)

p(x) = -x^2 +2x +24