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.
