Question 1003347
 {{{f(x) = -x^2 + 8x + 3}}}

the maximum value of the function will be {{{y}}} coordinate of vertex; so, write equation in vertex form  {{{f(x) = a(x-h)^2 + k}}}

 {{{f(x) = -(x^2 -8x) + 3}}}...........complete square

{{{f(x) = -1*(x^2 -8x+b^2)-(-1)b^2 + 3}}}

{{{f(x) = -(x^2 -8x+4^2)+1*4^2 + 3}}}

{{{f(x) = -(x -4)^2+16 + 3}}}

{{{f(x) = -(x -4)^2+19}}}

so, {{{h=4}}} and {{{k=19}}},vertex is at ({{{4}}}, {{{19}}})

=>the maximum value of the function will be {{{y=19}}}


{{{drawing( 600, 600, -10, 10, -10, 25,
circle(4,19,.12),locate(4,19,V(4,19)),
 graph( 600, 600, -10, 10, -10, 25, -(x -4)^2+19)) }}}