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

Question

Second -degree, with zeros of -6,and 1 goes to - infinity as x to - infinity

Answer 1

The factors that come from the zeros of -6 and 1 are

(x+6)(x-1)

Using FOIL you get the following second degree polynomial

x²-1x+6x-6

Combining like terms

x²+5x-6

In this form, as x goes to - infinity, this goes to + infinity. To make the parabola open downward instead of up, you reflect it on the x axis with a negative sign out in front.

-(x²+5x-6)

Simplified by distributing the -, you get

-x²-5x+6