help!!1

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. 

y=2x-4    y=x²-4

Answer 1

Step 1:

The equations are y = x² - 4 and y = 2x - 4 .

The quadratic equation y = x² - 4 represent the standard form of parabola y  = ax ²+ bx + c .

a  = 1 , b  = 0 , c = -4.

Axis of symmetry x = -b /2a  = 0/2 = 0.

To find vertex substiute x value in y = x² - 4.

y = 0 - 4  = -4

Vertex = (0, -4)

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

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

x	y = x² - 4	(x, y )
- 1	y =  (- 1)^2 -4= 1 -4 = -3	(- 1, -3)
- 2	y = (- 2)^2 -4= 4 -4 = 0	(- 2, 0)
0	y =(0)^2 -4= 0 -4 = -4	(0, -4)
1	y = (1)^2 -4= 1 -4 = -3	(1, -3)
2	y = (2)^2 -4= 4 -4 = 0	(2, 0)

Step 2:

y = 2x - 4

The equation y = 2x - 4 is in the form of  slope-intercept form y = mx + b.

slope = 2 and y-intercept is - 4.

y-intercept is - 4, so the line crosses the y-axis at (0, - 4)

Using slope find the next point.

Slope = rise/run = 2/1

Start at point (0, - 4), move 2 units up and 1 units right, then plot the point (1,-2).

Step 3:

Now graph the functions y = x² - 4 and y = 2x - 4 .

1.Draw a coordinate plane.

2.Plot the coordinate points.

3.Then sketch the graph, connecting the points with a smooth curve.

Step 4:

Observe the graph

The solutions of the equations y = x² - 4 and y = 2x - 4 are (0 , -4) and (2 , 0) .

Solutions:

The solutions  are (0 , -4) and (2 , 0) .