Question 78139
To find the vertex, lets complete the square and put the equation in vertex form:

*[invoke completing_the_square 1, 1, -6]

So the vertex is:

(-0.5, -6.25)



Now lets find the intercepts. The easiest way is to use the quadratic formula:

*[invoke quadratic "x", 1, 1, -6 ]

So the x-intercepts are x=2, x=-3

And here's the graph

{{{ graph( 300, 200, -6, 5, -10, 10, x^2+x-6) }}} graph of {{{y=x^2+x-6}}}