Answered

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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.

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Additional comment

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

View image sqdancefan
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