4.2-2 Constructing Polynomial Functions

1. 4.2-2 Constructing Polynomial Functions

2. Now, we have learned about several properties for polynomial functions • Finding y-intercepts • Finding x-intercepts (zeros) • End behavior (leading coefficient, degree) • Testing values for zeros/factors (synthetic division)

3. Knowing these properties, we can look to construct a polynomial given particular attributes • Locations of x/y intercepts • End behaviors (infinity, or negative infinity) • Degrees (largest power) • Specific coefficients

4. Remember, the value k is a zero, if and only if, x – k is a factor of p(x) • After constructing a polynomial, we can use our graphing calculators to help us verify

5. Example. Construct a polynomial with the following properties: Third degree, zeros of -3, 2, and 5, and as x -> ∞, f(x) -> - ∞

6. Example. Construct a polynomial with the following properties: fourth degree, zeros of -6, -4, 2, and a y-intercept of 18.

7. Example. Construct a polynomial with the following properties: zeros of 2, -3, and -4, fifth degree, y-intercept of 48, and as x -> ∞, f(x) -> - ∞

8. Take our your graphing calculators. We can now use them to help us confer/better put together our solutions.

9. Assignment • Pg. 322 • 49-56, ALL