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. 322• 49-56, ALL