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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

asked Jan 19, 2015 in PRECALCULUS by anonymous

1 Answer

0 votes

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) .

answered Jan 19, 2015 by yamin_math Mentor

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