Question 154762
Do you mean the vertex?



{{{(f*g)(x)}}} Start with the given expression



{{{f(x)*g(x)}}} Rewrite the function combination



{{{(x^2+4)*(x-3)}}} Plug in {{{f(x)=x^2+4}}} and {{{g(x)=x-3}}}




Now let's FOIL the expression.



Remember, when you FOIL an expression, you follow this procedure:



{{{(highlight(x^2)+4)(highlight(x)-3)}}} Multiply the <font color="red">F</font>irst terms:{{{(x^2)*(x)=x^3}}}.



{{{(highlight(x^2)+4)(x+highlight(-3))}}} Multiply the <font color="red">O</font>uter terms:{{{(x^2)*(-3)=-3*x^2}}}.



{{{(x^2+highlight(4))(highlight(x)-3)}}} Multiply the <font color="red">I</font>nner terms:{{{(4)*(x)=4*x}}}.



{{{(x^2+highlight(4))(x+highlight(-3))}}} Multiply the <font color="red">L</font>ast terms:{{{(4)*(-3)=-12}}}.



{{{x^3-3*x^2+4*x-12}}} Now collect every term to make a single expression.



So {{{(x^2+4)(x-3)}}} FOILs to {{{x^3-3*x^2+4*x-12}}}.



This means that {{{(f*g)(x)=x^3-3*x^2+4*x-12}}}



Since we're looking at a cubic, this means that the polynomial does not have a vertex. Are you sure that you have the right problem?