Question 465221
{{{f(x) = -2x^2+2x}}}

Remember that when the {{{x^2}}} in the parabola equation is {{{negative}}}, the parabola opens {{{downwards}}}. Therefore, it has a maximum value.

ANSWER: The quadratic function has a {{{MAXIMUM}}} value.

Remember that the vertex of a parabola occurs at ({{{h}}}, {{{k}}}).

Given: {{{f(x) = -2x^2+2x}}}
Means: {{{a = -2}}}, {{{b = 2}}}, {{{c=0}}}

{{{h = -b / 2a}}}

{{{h = -2 / 2(-2)}}}

{{{h = -2 / -4}}}

{{{h = 1 /2}}}


{{{k = (-b-4ac) / 4a}}}

{{{k = (-2-4(-2)*0) / 4(-2)}}}

{{{k = -2 /-8}}}

{{{k = 1/4}}}


the vertex: is at ({{{1 /2}}}, {{{1 /4}}})

{{{ graph( 500, 500, -5, 5, -10, 5, -2x^2+2x) }}}