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) About Me  (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)
y+=+x%5E2+%2B+6x

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 x+=+-b%2F%282a%29 (where a=1, b=6 as in the quadratic formula!) so x+=+-6%2F2+=+-3. 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
y+=+%28-3%29%5E2+%2B+6%28-3%29+=+9-18+=+-9.

graph+%28300%2C+300%2C+-10%2C+10%2C+-10%2C+10%2C+x%5E2+%2B+6x%29

R^2 at SCC