Q1. Given n+1 data pairs, a unique polynomial of degree ____ passes through the n+1 data points.
n+1
n
n or less
greater than n

Q2. Given the two points the linear Lagrange polynomial f₁(x) that passes through these two points is given by

Q3. The Lagrange polynomial that passes through three data points is given by

 The value of L₁(x) at x = 16 is

–0.071430
0.50000
0.57143
4.3333

Q4. The following data of the velocity of a body is given as a function of time.

A quadratic Lagrange interpolant is found using three data points, t=15, 18 and 22.  From this information, at what of the times given in seconds is the velocity of the body 26 m/s during the time interval of t=15 to 22 seconds.

20.173
21.858
21.167
22.020

Q5. The path that a robot is following on a x-y plane is found by interpolating four data points as

The length of the path from x = 2 to x = 7 is

Q6. The following data of the velocity of a body is given as a function of time.

 If you were going to use quadratic interpolation to find the value of the velocity at t=14.9 seconds, what three data points of time would you choose for interpolation?  Justify your answer.

0, 15, 18
15, 18, 22
0, 15, 22
0, 18, 24