Answer:
The correct option is D.
Step-by-step explanation:
From the given graph it is noticed that the line and parabola intersect each other at points (-6,7) and (-1,2). It means each equation of the system must be satisfied by these points.
If a line passing through two points, then the equation of line is
\(y-y_1=\frac{y_2-y_1}{x_2-x_1}(x-x_1)\)
The equation of line is
\(y-7=\frac{2-7}{-1-(-6)}(x-(-6))\)
\(y-7=-(x+6)\)
\(y-7=-x-6\)
\(y+x=1\) .... (1)
Therefore the equation of line is \(y+x=1\).
The standard form of the parabola is
\(y=a(x-h)^2+k\)
Where (h,k) is the vertex.
From the graph it is noticed that the vertex of the parabola is (-3,-2).
\(y=a(x+3)^2-2\)
The parabola passing through the point (-1,2).
\(2=a(-1+3)^2-2\)
\(2=4a-2\)
\(a=1\)
Therefore the equation of parabola is
\(y=(1)(x+3)^2-2=x^2+6x+9-2=x^2+6x+7\) .... (2)
So, the system of equations contains equation (1) and (2). Option D is correct.
