The system of equations are y = x 2 - 9 and y = - (x + 3)2 \ \

\

Step 1: \ \

\

Graph the two equations. \ \

\

Make the table of values to find ordered pairs that satisfy the equations. \ \

\

Choose values for x  and find the corresponding values for y. \ \

\ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \
\

x \ \

\ 		\

y = x 2 - 9 \ \

\ 		\

(x , y ) \ \

\
- 2y = (- 2)2 - 9 \ \ (- 2, - 5) \ \
- 1y = (- 1)2 - 9 \ \ (- 1, - 8)
\

1 \ \

\ 		\

y = ( 1)2 - 9 \ \

\ 		\

(1, - 8) \ \

\
\

2

\ 		\

y = (-2)2 - 9 \ \

\ 		\

(2, - 5) \ \

\
\

3 \ \

\ 		\

y = (3)2 - 9 \ \

\ 		\

(3, - 3) \ \

\
\

\ \

\ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \
\

x \ \

\ 		\

y = - (x + 3)2 \ \

\ 		\

(x , y ) \ \

\
-6 \ \ \

y = - (-6 + 3)2 \ \

\ 		(-6, -9) \ \
-4 \ \ \

y = - (-4 + 3)2 \ \

\ 		(-4, -1) \ \
\

-2 \ \

\ 		\

y = - (-2 + 3)2 \ \

\ 		\

(-2, -1) \ \

\
\

-1 \ \

\ 		\

y = - (-1 + 3)2 \ \

\ 		\

(-1, -4) \ \

\
\

1. Draw a coordinate plane.

\

2. Plot the points found in tables and draw a smooth curves through these points. \ \

\

 

\

\"\" \ \

\

Observe the graph the two curves are intersecting at \"\" and \"\". \ \

\

Solution: \ \

\

\"\" and \"\". \ \

\

Check: \ \

\

To check the solutions substitute the intersecting points in either of two equations. \ \

\

Substitute the point \"\" in \"\". \ \

\

\"\"

\

\"\" \ \

\

Since the above statement is true, \"\" is a solution of the quadratic system. \ \

\

Substitute the point \"\" in \"\". \ \

\

\"\" \ \

\

\"\" \ \

\

Since the above statement is true, \"\" is a solution of the quadratic system. \ \