Question 149596
First, we need to find the zeros. 



{{{(3-x)(5x + 35)=0}}} Set the expression equal to zero.




Now set each factor equal to zero:


{{{3-x=0}}} or  {{{5x + 35=0}}} 


Now solve for x for each factor:


{{{x=3}}} or  {{{x=-7}}} 


So the zeros of {{{(3-x)(5x + 35)}}} are {{{x=3}}} or  {{{x=-7}}}




Now average the zeros to get {{{(3+(-7))/2=(-4)/(2)=-2}}}



So the axis of symmetry (ie the x-coordinate of the vertex) is {{{x=-2}}}



Now plug in {{{x=-2}}} to find the y coordinate of the vertex 



{{{f(x)=(3-x)(5x + 35)}}} Start with the given function.




{{{f(-2)=(3-(-2))(5(-2) + 35)}}} Plug in {{{x=-2}}}



{{{f(-2)=(3+2)(5(-2) + 35)}}} Rewrite {{{3-(-2)}}} as {{{3+2}}}



{{{f(-2)=(3+2)(-10 + 35)}}} Multiply



{{{f(-2)=(5)(25)}}} Add



{{{f(-2)=125}}} Multiply



So the y coordinate of the vertex is {{{y=125}}}



This means that the vertex is at the point (-2,125). Since the vertex is either the highest or lowest point (in this case the highest), this means that that the maximum value of the function is {{{125}}}