GeoGebra

Polynomial Interpolation

Autor:Eda Kuluslu, Chad Kuhns, Steve Phelps
Thema:Algebra

Directions:

1. Enter points by typing, for example, “(3,0)” and ENTER in the Input: bar at the bottom. You should see this appear as "A=(3,0)" in the left column. 2. Type these additional points and ENTER after each one: (-1,0), (1,0), and (0,-3) 3. Type “Polynomial[A,B,C,D]” to see the interpolating polynomial for the points.

Polynomial interpolation

Question

What is the equation of the resulting polynomial?

Antwort überprüfen

Directions:

Create a polynomial using the process in Task 1 that has the following characteristics:
  • negative y-intercept
  • at least 3 x-intercepts
  • increasing over the interval (0,4)

Polynomial interpolation

Question

What is the equation of the polynomial you created?

Antwort überprüfen

Task 3

Move the blue points and observe how the equation changes. Then note your observations in the answer box below.

Question

How are the zeros related to the equation of the polynomial? Answer in 1-2 sentences.

Antwort überprüfen

Question

What happens to the curve when two blue dots overlap (are the same zero)? What happens to the corresponding factor in the equation? Answer in 2-3 sentences.

Question

What happens to the curve when three blue dots overlap (are the same zero)? What happens to the corresponding factor in the equation? Answer in 2-3 sentences.

Question

Make an observation between the relationship of each factor, its exponent, and what that means on the graph of the polynomial. Explain your observation below.

Question

Notice the y-intercept. How is the y-intercept affected as the zeros change? Answer in 1-2 sentences.

Question

Change the number of zeros. Make an observation between the number of zeros and the end behavior of the graph, and explain it in 2-3 sentences below.

Neue Materialien

Entdecke Materialien

Entdecke weitere Themen