Question

Solve (x - 2)^2 - 3 = 1 graphically. That is graph y = (x - 2)^2 - 3 and y = 1 on the same set of axes and find the x-value(s) of any points of intersection. Then use algebraic strategies to solve the equation and verify that your graphical solutions are correct.

Answer 1

Check the attachment(s) for the graphs pertaining to the question

No. 1) Check graph [first attachment]

No. 2) y = (x - 2)^2 - 3, y = 1

           (x - 2)^2 - 3 = 1,

           (x - 2)^2 = 4

            x - 2 = √4, x - 2 = - √4

            x = 4, x = 0

Substitute back to determine the respectively y-value:

y = (4 - 2)^2 - 3 = (2)^2 - 3 = 4 - 3 = 1

Check: y = (0 - 2)^2 - 3 = (-2)^2 - 3 = 4 - 3 = 1

So the points of intersection are (4, 1) and (0, 1). According to the graph, that is correct.