Question 756693

f(x)>=g(x)
{{{5^2>=19x-12}}}
{{{5x^2-19x+12>=0}}} THIS parabola has a minimum and opens upward.  Know that this parabolas is different from the given parabola in the question.


Try first checking discriminant.  Guess why?


{{{(-19)^2-4*5*12=19^2-240=121}}} which is positive.  We DO expect two roots.

{{{x=(19-sqrt(121))/(2*5)=(19-11)/10=4/5}}}
OR
{{{x=(19+sqrt(121))/(2*5)=(19+11)/10=3}}}


Knowing how this parabola appears and having the x-intercepts, the original statement is true for {{{x<=4/5}}} or for {{{x>=3}}}.


This intermediate parabola, not the originally given one:
{{{graph(300,300,-6,6,-9,9,5x^2-19x+12)}}}