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7: FINDING THE SIMPLEST FORM OF A POLYNOMIAL FUNCTION WHEN GIVEN THE X INTERCEPTS

EXAMPLE 1: QUADRATIC OPENING DOWNWARD

Write the simplest form of the function given by the graph: Graph

From x = (-4) --> (x+4); From x = 2--> (x-2)
Multiply the factors: (x+4)(x-2). Since the parabola is opening downward, multiply the whole function by (-1).
Final Answer: -(x+4)(x-2).

        EXAMPLE 2: POLYNOMIAL OF DEGREE 5



Graph
The x intercepts are (-4), (-2) and (1).
From x = (-4) the factor is (x+4).
From x = (-2) the factor is (x+2).
From x = (1) the factor is (x-1).

The function is the product (x+4)(x+2)(x-1).

Concept Check: Given that the zeros of a function are x = 0, x = 6 and x = (-3), write the simplest form of the function.