Which graph represents the solution set of y = x2 + 4x + 3 and y = 2x + 6?

graph a

graph b

graph c

graph d

Answer with explanation:

We have to find the point of Intersection of , parabola and line.

The given equation of Parabola is

 y= x²+4 x +3-----------(1)

The given equation of line is,

y =2 x +6----------(2)

Equating , (1) and (2), we get

x²+4 x +3=2 x +6

→x²+ 4 x - 2 x +3 -6=0

→x²+2 x -3=0

→x²+3 x - x -3=0

→x×(x+3)-1×(x+3)=0

→(x-1)(x+3)=0

→x-1=0  ∧ x+3=0

→x=1 ∧ x=-3

Substituting the value of , x in equation of line

x=1 gives, y =2 × 1 +6=8

x = -3, gives , y=2 × (-3) +6=-6+6=0

⇒Solution set,that is point of intersection of parabola and line is , (1,8) and (-3,0).

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