SOLUTION: 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

Algebra ->  Polynomials-and-rational-expressions -> SOLUTION: 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      Log On


   



Question 1186730: 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 by MathLover1(20850) About Me  (Show Source):
You can put this solution on YOUR website!

Second-degree, with zeros of x%5B1%5D=-4 and x%5B2%5D=6, and goes
to −∞ as x→−∞.
p%28x%29+=%28x-x%5B1%5D%29%28x-x%5B2%5D%29
p%28x%29+=%28x-%28-4%29%29%28x-6%29
p%28x%29+=%28x%2B4%29%28x-6%29
p%28x%29+=x%5E2+-+2x+-+24
for the condition that y→ −∞ as x→ −∞
we require the coefficient of x^2 to be negative
p%28x%29+=-%28x%5E2+-+2x+-+24%29
p%28x%29+=-x%5E2+%2B+2x+%2B+24 is the required polynomial

+graph%28+600%2C+600%2C+-10%2C+10%2C+-10%2C+30%2C+-x%5E2+%2B2x%2B24%29+