Question 222527
{{{f(x) = 2x^2 + 2x - 6 }}}
.
From the coefficient associated with the x^2 term, in this case, it's a POSITIVE TWO.  Since it is "positive" think "smiley face"-- so, it's a parabola that's opens upwards.  If it was "negative" think "sad face" -- so, it's a parabola that's opens downwards.
.
Since the coefficient is +2, it opens upwards thus the function will have a MINIMUM.
.
One way to find the vertex, is by completing the square.  Doing so you will get it into the "vertex form" of the equation:
y= a(x-h)2+k
where
(h,,k) is the vertex
.
{{{f(x) = 2x^2 + 2x - 6 }}}
{{{f(x) = 2(x^2 + x + __)  - 6 }}}
{{{f(x) = 2(x^2 + x + 1/4 )  - 6 - 1/2}}}
{{{f(x) = 2(x + 1/2)^2  - 13/2 }}}
{{{f(x) = 2(x - (-1/2))^2  + (-13/2)}}}
.
Therefore, the vertex is at (-1/2, -13/2)
or
(-.5, -6.5)