Construct a polynomial function with the stated properties. Reduce all fractions to lowest terms. Second-degree, with zeros of −1 and 3 , and goes to −∞ as x→−∞.

Answer 1

-(x+1)(x-3) = -(x^2 -2x -3)

f(x) = y = -x^2 +2x +3 is a 2nd degree polynomial function with zeros -1 and 3.

the degree is the exponent of the highest powered term = 2

it's a downward opening parabola where y approaches negative infinity as x approaches negative infinity

it has zeros when x+1=0, x=-1

and when x-3=0, x=3

-1 and 3 are the x intercepts where y=0

the vertex has an x coordinate midway between the zeros, at (3-1)/2 = 2/2 = 1

(1, f(1)) =(1,4) = vertex = maximum point

try graphing it with an online graphing calculator such as desmos or a handheld calculator, to visually see the x intercept (zeros) and left side behavior as x and f(x) go approach negative infinity