Which graph shows the system (x^2 = y =2 x^2 + y^2 = 9

The graph of given system of equations is shown below.

Step-by-step explanation:

Consider the given system of equations

We need to find the graph of the given system of equations.

The first equation can be rewritten as

It is the vertex form of a parabola where, (h,k) is vertex and a is a constant.

In the above equation h=0 and k=2, it means vertex of the parabola is (0,2).

Leading coefficient is negative in means it is a downward parabola. The table of values is

x :    -2         -1         0         1         2

y :    -2          1         2         1         -2

Plot these points on a coordinate plane and connect them by a free hand curve.

The second equation can be rewritten as

It is the standard form of a circle where, (h,k) is center of the circle and r is the radius.

In the above equation h=0,k=0,r=3. So, it is a circle with radius 3 and centered at (0,0).