SOLUTION: If two numbers differ by 6, then what is the least possible value of their product?
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Question 11856: If two numbers differ by 6, then what is the least possible value of their product?
Answer by rapaljer(4671) (Show Source): You can put this solution on YOUR website!
Let x = first number
x+6 = second number
Let y = product of the numbers
y = x(x+6)
Graph the equation of this parabola, and find the lowest value of y, which is the vertex of the parabola. Algebraically, the vertex will always be at (where a=1, b=6 as in the quadratic formula!) so . Also halfway between the x intercepts, which would be at x=0 and x= -6. The minimum value of the product of the numbers would be
.
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