Question

Which graph represents the function f(x) = x2 + 3x + 2?

Answer 1

Answer:

Graph 1

Step-by-step explanation:

Here, the given equation is,

$f(x)=x^2+3x+2-----(1)$

For x-intercept, f(x) = 0

$x^2+3x+2=0$

$x^2+2x+x+2=0$

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

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

$\implies x=-1\text{ or } -2$

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.

Answer 2

Graph 1 obviously because it states x^2 meaning it is a quadratic function. This one requires very little explanation and it is instinctive given the parabola. The other graphs are linear or to the x power.