compare properties of the two functions determine if the functions have minimum

Algebra
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or maximum values and their zeros are real or complex  show work. function f(x) 5 less than 3 times the square of a number increased by 4 times the number.    function g(x): 5 more than the opposite of 3 times the square of a number increased by 4 times the number 

May 1st, 2015

Converting to formulae: f(x)=3x^2-5+4x.   g(x)=5-3x^2+4x     . Putting in descending powers,

f(x)=3x^2+4x-5  ; g(x)=-3x^2+4x+5     . Because the quadratic term dominates as |x| goes to infinity, it is clear that f is concave up whereas g is concave down. Thus f has a minimum whereas g has a maximum. f must have real zeroes because when x=0 f is negative, and f assumes positive values. Thus it must cross the x axis to get there. Similarly, g has real zeroes because when x=0 g is positive but g assumes negative values and must cross the x axis to get there. 

May 1st, 2015

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