we are given
[tex] f(x)=x^2+3x+2 [/tex]
x-intercept:
we can set f(x)=0
and then we can solve for x
[tex] x^2+3x+2=0 [/tex]
[tex] (x+1)(x+2)=0 [/tex]
[tex] x=-1,x=-2 [/tex]
y-intercept:
now, we can plug x=0
[tex] y=0^2+3(0)+2 [/tex]
[tex] y=2 [/tex]
Vertex:
[tex] x=-\frac{b}{2a} [/tex]
[tex] x=\frac{-3}{2*1} [/tex]
[tex] x=-\frac{3}{2} [/tex]
[tex] f(-\frac{3}{2} )=(-\frac{3}{2} )^2+3*(-\frac{3}{2} )+2 [/tex]
[tex] y=-0.25 [/tex]
so, vertex is (-1.5 , -0.25)
so, we can draw graph
