Upside-down Parabola

I know that placing a minus sign in front of x^2 for y = x^2 forms an upside-down U on the xy-place. Why does this happen? Why does a minus invert the parabola on the xy-plane?

 

y = -x^2

make table:
x|y
-2|-4....................y = -(-2)^2=-4
-1|-1....................y = -(-1)^2=-1
0|0....................y = -(0)^2=0
1|-1....................y = -(1)^2=-1
2|-4....................y = -(2)^2=-4

make conclusion why parabola is upside-down

 

Based on the table the parabola is upside-down because the x-and y-coordinates change signs. Yes?

 

because the y-coordinates are all negative

 

Interesting concept.