Question

The graph represents the function f(x)=x^2+3x+2

Answer 1

we are given

`f(x)=x^2+3x+2`

x-intercept:

we can set f(x)=0

and then we can solve for x

`x^2+3x+2=0`

`(x+1)(x+2)=0`

`x=-1,x=-2`

y-intercept:

now, we can plug x=0

`y=0^2+3(0)+2`

`y=2`

Vertex:

`x=-(b)/(2a)`

`x=(-3)/(2*1)`

`x=-(3)/(2)`

`f(-(3)/(2) )=(-(3)/(2) )^2+3*(-(3)/(2) )+2`

`y=-0.25`

so, vertex is (-1.5 , -0.25)

so, we can draw graph