DISCUSS: Polynomials Determined by a Set of Points We all know that two points uniquely determine a line y = ax + b in the coordinate plane. Similarly, three points uniquely determine a quadratic (second-degree) polynomial y = ax? + bx + c four points uniquely determine a cubic (third-degree) polynomial y = ax' + bx? + cx + d and so on. (Some exceptions to this rule are if the three points actually lie on a line, or the four points lie on a quadratic or line, and so on.) For the following set of five points, find the line that contains the first two points, the quadratic that con- tains the first three points, the cubic that contains the first four points, and the fourth-degree polynomial that contains all five points. (0,0), (1, 12), (2, 40), (3, 6), (-1, –14) Graph the points and functions in the same viewing rectangle using a graphing device.

DISCUSS: Polynomials Determined by a Set of Points We all know that two points uniquely determine a line y = ax + b in the coordinate plane. Similarly, three points uniquely determine a quadratic (second-degree) polynomial y = ax? + bx + c four points uniquely determine a cubic (third-degree) polynomial y = ax' + bx? + cx + d and so on. (Some exceptions to this rule are if the three points actually lie on a line, or the four points lie on a quadratic or line, and so on.) For the following set of five points, find the line that contains the first two points, the quadratic that con- tains the first three points, the cubic that contains the first four points, and the fourth-degree polynomial that contains all five points. (0,0), (1, 12), (2, 40), (3, 6), (-1, –14) Graph the points and functions in the same viewing rectangle using a graphing device.

Algebra and Trigonometry (6th Edition)

6th Edition

ISBN:9780134463216

Author:Robert F. Blitzer

Publisher:Robert F. Blitzer

ChapterP: Prerequisites: Fundamental Concepts Of Algebra

Section: Chapter Questions

Problem 1MCCP: In Exercises 1-25, simplify the given expression or perform the indicated operation (and simplify,...

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Question

DISCUSS: Polynomials Determined by a Set of Points We all
know that two points uniquely determine a line y = ax + b
in the coordinate plane. Similarly, three points uniquely
determine a quadratic (second-degree) polynomial
y = ax? + bx + c
four points uniquely determine a cubic (third-degree)
polynomial
y = ax' + bx? + cx + d
and so on. (Some exceptions to this rule are if the three points
actually lie on a line, or the four points lie on a quadratic or
line, and so on.) For the following set of five points, find the
line that contains the first two points, the quadratic that con-
tains the first three points, the cubic that contains the first
four points, and the fourth-degree polynomial that contains
all five points.
(0,0),
(1, 12), (2, 40), (3, 6), (-1, –14)
Graph the points and functions in the same viewing rectangle
using a graphing device.

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