Question 689719
The x-coordinate of the vertex is at {{{ -b/(2a) }}}
when the equation is in the form {{{ y = a*x^2 + b*x + c }}}
In your case,
{{{ y=x^2+4x+5 }}}
{{{ a = 1 }}}
{{{ b = 4 }}}
{{{ -b/(2a) = -4/(2*1) }}}
{{{ -b/(2a) = -2 }}}
So now you know the vertex is at (-2,y)
To find {{{ y }}}, plug {{{ x = -2 }}}
into the equation
{{{ y = (-2)^2 + 4*(-2) + 5 }}}
{{{ y = 4 - 8 + 5 }}}
{{{ y = 1 }}}
The vertex is at (-2,1)
Here's a plot of the equation:
{{{ graph( 400, 400, -7, 3, -2, 10, x^2 + 4x + 5 ) }}}