Solve the following sysstem of equations by graphing:

Question

y = x^2 - 4 and y = x - 2.
Thanks,

Answer 1

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

Write equation 1 : y = x ² - 4 in complete square form.

y = (x - 0)² - 2.

The above equation represent the parabola.

Compare the equation y = (x - 0)² - 2. with standard from from the of the equation of a parabola with vertex (h, k ) and axis of symmetry x = h is y = a(x - h )² + k.

Vertex (h, k ) = (0, 2), and axis of symmetry h = 0.

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		(x, y)
1
2
0
-1
-2

The points (1,- 3), (2, 0), (0, - 4), (- 1, - 3) and (- 2, 0) are also on the parabola.

1.Draw a coordinate plane.

2.Plot the coordinate points.

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

Answer 2

Contd....

Write equation 2 :  y = x - 2.

Write the equation in slope-intercept form y = mx + b, where m is slope and b is y-intercept.

The equation is y = x - 2.

It is already in slope - intercept - form.

Compare the equation with slope-intercept form y = mx + b.

slope = 1 and y - intercept is - 2.

y - intercept is - 2, so the line crosses the y - axis at (0, - 2)

Using slope find the next point.

Slope = rise/run = 1/1

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

Draw a line through these points

Find the solution points  by graphically.

Observe the graph, the solution points are (- 1, - 3) and (2, 0).