Question 1091440
{{{f(x) = -4x^2 - 24x + 15 }}}

The function has a maximum since the first term {{{-4x^2}}} has a negative coefficient. 

To find the max, you need to find the axis of symmetry first, and to find the axis of symmetry, use this formula:

{{{x=-b/(2a)}}}


From the equation {{{f(x) = -4x^2 - 24x + 15}}} we can see that {{{a=-4}}} and {{{b=-24}}}

{{{x=-(-24)/(2*-4)}}} 

{{{x=24/(-8)}}} 

{{{x= -3}}} 

So the axis of symmetry is  {{{x=-3}}}, and it is the x-coordinate of the vertex is {{{x=-3}}}.

 Lets plug this into the equation to find the y-coordinate of the vertex.

Lets evaluate {{{f(-3)}}}

{{{f(-3)=-4*(-3)^2 - 24*(-3) + 15}}} 

{{{f(3)=-36 +72 + 15}}} 

{{{f(3)=51}}} 

So the vertex is ({{{-3}}},{{{51}}})

So that means the functions highest value is {{{51}}}  which means the functions maximum is:{{{51}}} 

{{{drawing(600,600,-15,10,-10,55,
circle(-3,51,.13), locate(-3,51,V(-3,51)),
graph(600,600,-15,10,-10,55, -4x^2 - 24x + 15))}}}



2.
{{{f(x) = 6x^2 + 36x - 20}}}

The function has a minimum since the first term {{{6x^2}}} has a positive coefficient. 

To find the min, you need to find the axis of symmetry first:

{{{x=-b/(2a)}}}

{{{x=-36/(2*6)}}}

{{{x=-36/12}}}

{{{x=-3}}}

So the axis of symmetry is  {{{x=-3}}}, and it is the x-coordinate of the vertex is {{{x=-3}}}.

 Lets plug this into the equation to find the y-coordinate of the vertex.

Lets evaluate {{{f(-3)}}

{{{f(x) = 6(-3)^2 + 36(-3) - 20}}}

{{{f(x) = 54 -108 - 20}}}

{{{f(x) =  -74}}}

So the vertex is ({{{-3}}},{{{-74}}})

So that means the functions highest value is {{{-74}}}  which means the functions maximum is:{{{-74}}} 

{{{drawing(600,600,-10,10,-100,10,
circle(-3,-74,.13), locate(-3,-74,V(-3,-74)),
graph(600,600,-10,10,-100,10, 6x^2 + 36x - 20 ))}}}