Question 518220
The vertex is at {{{ -b/(2a) }}}
{{{ a = 3 }}}
{{{ b = -2 }}}
{{{ x[v] = -b/(2a) }}}
{{{ -b/(2a) = -(-2)/(2*3) }}}
{{{ -b/(2a) = 1/3 }}}
{{{ y[v] = 3*(1/3)^2 - 2*(1/3) + 1 }}}
{{{ y[v] = 1/3 - 2/3 + 3/3 }}}
{{{ y[v] = 2/3 }}}
The vertex is at ( 1/3, 2/3 )
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y-intercept:
{{{ y = 3x^2 - 2x + 1 }}}
{{{ y = 3*0 - 2*0 + 1 }}}
( 0,1)
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x-intercept:
{{{ 3x^2 - 2x + 1 = 0 }}}
Use quadratic formula
{{{x = (-b +- sqrt( b^2-4*a*c ))/(2*a) }}} 
{{{ a = 3 }}}
{{{ b = -2 }}}
{{{ c = 1 }}}
{{{x = (-(-2) +- sqrt( (-2)^2-4*3*1 ))/(2*3) }}} 
{{{x = ( 2 +- sqrt( 4 - 12 )) / 6 }}} 
{{{ x = ( 2 +- 2*sqrt(2)*i ) / 6 }}}
{{{ x = ( 1 +- sqrt(2)*i ) / 3 }}}
There is no x-intercept, since both
roots are complx numbers
Here's a plot:
{{{ graph( 400, 400, -4, 4, -2, 10, 3x^2 - 2x + 1) }}}