Algebra

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

This forms a parabola that opens upward, therefore the    

range is from the vertex's y-coordinate to positive infinity.    

y  =  (6x + 7)(2x – 3)  =  12x² – 4x – 21    

y'  =  24x – 4     

set y' = 0     —>>  x = 1/6     & sub back into original    

y  =  [(12) • (1/6)²]  –  (4)(1/6)  –  21    

y  =  1/3                 – 2/3           – 21   =  – 21.3333    

The range is from – 21.3333 to positive infinity    

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