Solve the equation |x-2|-3=0 first by finding the zeros of
y=|x-2|-3 and then algebraically.

The solution of given equation are -1 and 5.

Step-by-step explanation:

The given equation is

We need to solve the above equation by finding the zeros of

The vertex form of an absolute function is

where, a is constant and (h,k) is vertex.

Here, h=2, k=-3. So vertex of the function is (2,-3).

The table of values is

   x           y

   0         -1

   2         -3

   4         -1

Plot these points on a coordinate plane and draw a V-shaped curve with vertex at (2,-3).

From the given graph it is clear that the graph intersect x-axis at -1 and 5. So, zeroes of the function y=|x-2|-3 are -1 and 5.

Therefore the solution of given equation are -1 and 5.

Now solve the given equation algebraically.

Add 3 on both sides.

Add 2 on both sides.

and

and

Therefore the solution of given equation are -1 and 5.

2

step-by-step explanation: