Question

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

Answer 1

The graph of given system of equations is shown below.

Explanation:

Consider the given system of equations

`x^2+y=2`

`x^2+y^2=9`

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

The first equation can be rewritten as

`y=-x^2+2`

It is the vertex form of a parabola
`y=a(x-h)^2+k` 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

`x^2+y^2=3^2`

It is the standard form of a circle
`(x-h)^2+(y-k)^2=r^2` 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).