Question 358742
{{{ y = 2x^2 - 12x + 27 }}}
Complete the square to get to vertex form, {{{y=a(x-h)^2+k}}}.
{{{y=2(x^2-6x)+27}}}
{{{y=2(x^2-6x+9)+27-2(9)}}}
{{{y=2(x-3)^2+27-18}}}
{{{highlight(y=2(x-3)^2+9)}}}
Since {{{a>0}}}, the parabola opens upwards and the vertex value is a minimum.
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{{{y[min]=9}}}
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Domain:  ({{{-infinity}}},{{{infinity}}})
Range : ({{{9}}},{{{infinity}}})
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{{{drawing(300,300,-10,10,-5,15,grid(1),circle(3,9,0.3),blue(line(3,-10,3,200)),graph(300,300,-10,10,-5,15,2(x-3)^2+9,2x^2-12x+27))}}}