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It was inevitable, but my one of daughter's math problems has me stumped ;(

I need to find the Rule:

x= 0|1|2|4

Y=-2|2|-2|-2

The given values are (0,-2), (1,2), (2,-2), and (4,-2).

Add 2 to all the y values at first and get (0,0), (1,4), (2,0), and (4,0).

To fit these values, the equation should be f(x) = A(x-0)(x-2)(x-4).

Clearly, if x=0, x=2, or x=4, the equation gives a value of 0, as it should.

At x=1, the value f(1) = A(1)(-1)(-3) = 3A.

Since we need 3A = 4, we need A = 4/3.

This gives us the equation f(x) = 4x(x-2)(x-4)/3.

Since we know that (x-2)(x-4) is x² -6x + 8, the equation is (4x³ - 24x² + 32x)/3.

Putting in 0, 1, 2 and 4 for x gives, in order, 0, 4, 0, and 0.

Since the values are suppose to be -2, 2, -2, -2, it can be seen we need to subtract of 2.

Since 2 = 6/3, the final equation is (4x³ - 24x² + 32x - 6)/3.

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