SOLUTION: Find a cubic polynomial function f(x) that satisfies both of the following conditions: a. f(x) has rational zeros 1 and 2 b. f(0) = 1 and f(-1) = 4

Question 1172076: Find a cubic polynomial function f(x) that satisfies both of the following conditions:
a. f(x) has rational zeros 1 and 2
b. f(0) = 1 and f(-1) = 4
Answer by htmentor(1343) (Show Source): You can put this solution on YOUR website!
The cubic has 3 factors of degree 1. Since there are zeros at 1 and 2, it
can be written as f(x) = (ax + b)(x - 1)(x - 2). We can use the information
provided in b. to solve for a and b. f(0) = 1 -> b(-1)(-2) = 1 -> b = 1/2
f(-1) = 4 = (-a + 1/2)(-2)(-3) = 4 -> 1/2 - a = 4/6 -> a = -1/6.
Thus, f(x) = (-x/6 + 1/2)(x - 1)(x - 2). I will leave it to you to express
it in standard form. The graph is below:

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