Answer:
Graph 1
Step-by-step explanation:
Here, the given equation is,
[tex]f(x)=x^2+3x+2-----(1)[/tex]
For x-intercept, f(x) = 0
[tex]x^2+3x+2=0[/tex]
[tex]x^2+2x+x+2=0[/tex]
[tex]x(x+2)+1(x+2)=0[/tex]
[tex](x+1)(x+2)=0[/tex]
[tex]\implies x=-1\text{ or } -2[/tex]
So, the x-intercept of the function are (-1,0) and (-2,0)
Since, the line must has at least one x-intercept.
⇒ Graph 2 and Graph 4 can not be the graph of the given function,
Also, for y-intercept,
Put x = 0 in equation (1),
We get, f(x) = 2,
Hence, the y-intercept of the given function is (0,2),
But in Graph 3 the y-intercept of the function = (0,1)
⇒ Graph 3 can not be the graph of the given function,
Therefore, Graph 1 is the correct graph of the given function.
