Question 1108738
{{{y=2x-7x^2}}} you are given the parabola opens downwards ({{{a}}} is negative number), and it has a maximum at vertex

so, {{{y}}} coordinate of the vertex will be greatest value of the range

now find the coordinates of the vertex: 

The {{{x}}}-coordinate of the vertex can be found by the formula {{{-b/2a}}}, and to get the y value of the vertex, just substitute {{{-b/2a}}}, into the {{{y=2x-7x^2}}}

you have {{{a=-7}}} and {{{b=2}}}

{{{-b/2a=-2/(2(-7))=2/14=1/7}}}

{{{y=2(1/7)-7(1/7)^2}}}

{{{y=2/7-cross(7)1(1/cross(49)7)}}}

{{{y=2/7-1/7}}}

{{{y=1/7}}}

so, the vertex is at ({{{1/7}}},{{{1/7}}})

and the range is:

{ {{{y}}} element {{{R}}} : {{{y<=1/7}}} }


{{{drawing( 600, 600, -5, 5, -5, 5,
circle(1/7,1/7,.011),locate(1/7,1/2,v(1/7,1/7)),
green(line(0,1/7,0,-5)),
 graph( 600, 600, -5, 5, -5, 5, 2x-7x^2)) }}}