4.2-2 Constructing Polynomial Functions

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)

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

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

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

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

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) -> - ∞

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

Assignment Pg , ALL