Answered

Welcome to Westonci.ca, your ultimate destination for finding answers to a wide range of questions from experts. Discover the answers you need from a community of experts ready to help you with their knowledge and experience in various fields. Join our platform to connect with experts ready to provide precise answers to your questions in different areas.

f(x)=ax³+2x²+bx+c, given that f(0)=3 and f(1)=4. Determine the value of a, b and c

Sagot :

sqdancefan

Answer:

  • a = any real number
  • b = -a-1
  • c = 3

Step-by-step explanation:

You want the values of a, b, c in the cubic function f(x)=ax³+2x²+bx+c, given the graph contains points (0, 3) and (1, 4).

Underspecified

The given function has three (3) variable values we are to find. The given points provide two (2) constraints, not enough constraints to specify the function completely. This means there are infinitely many suitable sets of values of 'a' and 'b'.

Equations

In order for the graph to go through the given points, we must have ...

  f(0) = 3 = a·0³ +2·0² +b·0 +c   ⇒   c = 3

  f(1) = 4 = a·1³ +2·1² + b·1 +3   ⇒   a +b = -1

The value of 'a' can be anything you like. The value of 'b' must be (-a-1). The value of 'c' is 3.

__

Additional comment

The attached graph shows the function for a=1 and a=-2.

View image sqdancefan
We hope our answers were useful. Return anytime for more information and answers to any other questions you have. We hope this was helpful. Please come back whenever you need more information or answers to your queries. Thank you for using Westonci.ca. Come back for more in-depth answers to all your queries.