Question 906422
Let {{{f (x) =  x^2 + 4x  -  7 }}}...as you can see, {{{a=1}}}, {{{b=4}}}, and {{{c=-7}}}

(a) Find the coordinates of the vertex.

{{{x=-b/2a}}} is x-coordinate of the {{{vertex}}}
so,
 {{{x=-b/2a=-4/2*1=-4/2=-2}}}

 and, to find the y-coordinate that goes with it,use that value for x in our equation

{{{f (x) =  x^2 + 4x  -  7 }}} ...solve for {{{f(x)}}} which is equal to {{{y}}}

{{{y =  (-2)^2 + 4(-2)  -  7 }}}

{{{y =  4 -8  -  7 }}}

{{{y =   -4 -  7 }}}

{{{y =-11 }}}

so, the coordinates of the vertex are:( {{{-2}}} ,{{{-11}}})

(b) The [Either max/min] value of f is 

 the max or min of a parabola is always the vertex 

{{{f ( -2 ) = -11 }}}

(c) Find the domain and range of f 

the domain: {{{R}}}  (all real numbers)
the range: { {{{y}}} element {{{R}}} : {{{y>=-11}}} }