Question 60403
Find the vertex and intercepts for each parabola. Sketch the graph

44. g(x) = x^2 + x – 6
:
The y-intercept is when x=0
g(0)=0^2+0-6
g(0)=-6 
The y-intercept is: (0,-6)
:
The x-intercept happens when g(x)=0
0=x^2+x-6  Factor
0=(x+3)(x-2)
x+3=0  and x-2=0
x=-3  and  x=2
The x intercepts are: (-3,0) and (2,0)
:
The x value of the vertex is found with the formula {{{highlight(x=-b/2a)}}}
a=1, b=1. and c=-6
{{{x=-1/(2(1))}}}
x=-1/2
Find the y-value by finding g(-1/2)
g(-1/2)=(-1/2)^2+(-1/2)-6
g(-1/2)=1/4-1/2-6
g(-1/2)=1/4-2/4-24/4
g(-1/2)=-25/4
The vertex is (-1/2,-25/4)
:
{{{graph(300,200,-10,10,-10,10,x^2+x-6)}}}
Happy Calculating!!!