helpp!2

Question

show how to solve the system of equation graphically using the grid below. make sure you clearly state your solution(s) and show how to check. sorry about my graph but something like that

y=x²-9   y=-(x+3)² 

Answer 1

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

The quadratic equations represents a parabola in the graph.

Step 1:

To graph the two equations we need some points through the curves.

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

 

Comments

Contd...

Step 2:

Graph:

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 .

Step 3:

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.

Solution:

and .