Find the minimum product of two numbers whose difference is nine.

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If you are not limited to positive numbers or integers, you would be locating the vertex of the parabola using the parabolic equation:

y = ax^2 + bx + c

In this case we have:

y = x(x+9)

y = x^2 + 9x

The x coordinate of the vertex is found by using the equation:

-b/2a

In this case b is 9 and a is 1, so

-9/2 = -4.5

The minimum value will be when x = -4.5 and x + 9 = 4.5, so:

-4.5*4.5 = -20.25

-20.25 is the minimum product.

-20.25

Assuming we aren't dealing with negative or fractional numbers, the smallest product would have to be 0. The numbers 9 and 0 have a difference of 9 and when multiplied together the product is 0.

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