SOLUTION: Learning to find Maximum and Minimum Values for Applications of Quadratic Functions in my Algebra class and the only question on my homework that is giving me trouble is this one:

Question 1117979: Learning to find Maximum and Minimum Values for Applications of Quadratic Functions in my Algebra class and the only question on my homework that is giving me trouble is this one:
One number is 6 less than twice a second number. Find a pair of such numbers so that their product is as small as possible.
The two numbers are:
The smallest possible product is:
I can't seem to figure out how to set the equation up. Please help!
Answer by Podrius(1) (Show Source): You can put this solution on YOUR website!
Let x = first number
Let y = second number
In terms of x: y=2x-6
The product of x and y:
Then expanded: 2x^2-6x
Then find the vertex:
x=1.5
Then, solve for y: y=2(1.5)-6
y=-3
So, the two numbers are: (1.5,-3)
And, the smallest possible product is: 1.5(-3) = -4.5
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