Question 1206757


 {{{y = -x^2 - 2x + 3}}}

you have an upside down parabola which have a max at vertex, so the range will be all {{{y}}} less and equal to the {{{y}}} coordinate of the vertex

find vertex

 {{{y = -(x^2 +2x+b^2)-(-b^2) + 3}}}....{{{b=1}}}


 {{{y = -(x^2 +2x+1^2)+1^2 + 3}}}

 {{{y = -(x+1)^2+4}}}


vertex is at ({{{-1}}},{{{4}}})

so, the range is

{ {{{y}}} element {{{R}}} : {{{y<=4}}} }


{{{ graph( 600, 600, -10, 5, -10, 10, -x^2 - 2x + 3) }}}


answer: C. {{{y<=4}}}