Question 29915
Determine whether the graph of the parabola opens upward or downward.
{{{g(x) = x^2+x-6}}}

If the coefficient of the {{{x^2}}}term is positive, the parabola opens upward, if it is negative, then it opens downward.

In this case, the coefficient is +1 so the parabola opens upward.

If you want to find the location of the vertex of the parabola, then you can use the fact that the x-coordinate of the vertex is given by:
{{{x = -b/2a}}} a = 1 and b = 1, so:
{{{x = -1/2}}} now substitute this value of x into the original equation and solve for g(x).
{{{g(x) = (-1/2)^2+(-1/2)-6}}}
{{{g(x) = (1/4)-(1/2)-6}}}
{{{g(x) = -6.25}}}

The vertex is located at:(-0.5, -6.25)

Here's the graph:
{{{graph(300,200,-5,5,-8,4,x^2+x-6)}}}