finding polynomial (Math help)

Question

an example of a polynomial with 2 zeros that has “both down” end behavior.

Answer 1

-x^2+2x-3 is one of many equations that satisfy those conditions.

Any quadratic equation in the form ax^2+bx+c with the following conditions.

b^2-4ac>0. If the descriminate is greater then zero you will have two real solutions or two zeros.

Since you need the end behavior to both point downward. Let a<0 or in other words put any negitive real number for the coefficient of x^2.

Answer 2

The end behavior of a polynomial is based on two characteristics of the polynomial: the degree of the polynomial and the sign of the leading coefficient.

If the degree is even and the leading coefficient is positive, the graph rises on both the left and the right.

If the degree is even and the leading coefficient is negative, the graph falls on both the left and the right.

If the degree is odd and the leading coefficient is positive, the graph falls on the left and rises on the right.

If the degree is odd and the leading coefficient is negative, the graph rises on the left and falls on the right.

Feel free to comment if you have any more questions!