Answer
Vertex: $(-1/2, -25/4)$
Opens upward
x-intercepts: -3, 2
y-intercept: -6
Work Step by Step
$f(x)=x^2+x-6$
Vertex: $-b/2a=x$
$x=-(1)/2*1$
$x=-1/2$
$f(x)=x^2+x-6$
$f(-1/2)=(-1/2)^2+(-1/2)-6$
$f(-1/2)=1/4-1/2-6$
$f(-1/2)=-25/4$
Vertex: $(-1/2, -25/4)$
Opens upward
$x=0$
$f(x)=x^2+x-6$
$f(0)=0^2+0-6$
$f(0)=0+0-6$
$f(0)=-6$
$y=0$
$f(x)=x^2+x-6$
$0=x^2+x-6$
$0=(x+3)(x-2)$
$x+3=0$
$x+3-3=0-3$
$x=-3$
$x-2=0$
$x-2+2=0+2$
$x=2$
x-intercepts: -3, 2
y-intercept: -6
