SOLUTION: What is the range of the function g(x) = (6x + 7)(2x - 3)?

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Question 1209603: What is the range of the function g(x) = (6x + 7)(2x - 3)?
Answer by Edwin McCravy(20056) About Me  (Show Source):
You can put this solution on YOUR website!
g(x) = (6x + 7)(2x - 3)

This is a parabola opening upward.

Its range will be [y coordinate of vertex, infinity)

g%28x%29+=+%286x+%2B+7%29%282x+-+3%29
g%28x%29+=+12x%5E2-4x-21

a=12, b=-4, c=-21

Use the vertex formula

Range = 

Range = 

Range = matrix%281%2C5%2C%0D%0A%0D%0A%22%5B%22%2Cg%284%2F24%29%2C%22%2C%22%2Cinfinity%2C%22%29%22%29 

Range = matrix%281%2C5%2C%0D%0A%0D%0A%22%5B%22%2Cg%281%2F6%29%2C%22%2C%22%2Cinfinity%2C%22%29%22%29

g%28x%29+=+12x%5E2-4x-21
g%281%2F6%29+=+12%281%2F6%29%5E2-4%281%2F6%29-21
g%28x%29+=+12%281%2F36%29-2%2F3-21
g%28x%29+=+1%2F3-2%2F3-63%2F3
g%28x%29+=+-64%2F3

Range = matrix%281%2C5%2C%0D%0A%0D%0A%22%5B%22%2C-64%2F3%2C%22%2C%22%2Cinfinity%2C%22%29%22%29

Edwin