Question 558969
{{{ y = x^2 + 6x + 9 }}}
I know that the curve has a minimum and not
a maximum because the coefficient of the {{{ x^2 }}} term
is (+) and not (-)
The form of the equation is {{{ ax^2 + bx + c }}}
The {{{x}}} coordinate of the minimum is at
{{{ x[min] = -b/(2a) }}}
{{{ x[min] = (-6)/(2*1) }}}
{{{ x[min] = -3 }}}
Now plug this back into the equation to get {{{ y[min] }}}
{{{ y[min] = (-3)^2 + 6*(-3) + 9 }}}
{{{ y[min] = 9 - 18 + 9 }}}
{{{ y[min] = 0 }}}
The minimum is at (-3,0)
Here's the plot:
{{{ graph( 400, 400, -5, 5, -5, 5, x^2 + 6x + 9 ) }}}