Create functions of the left-hand side and right-hand side, and enter them into a graphing calculator.
x=1 and x=6, see solution.
Practice makes perfect
To solve this equation graphically we will treat each side as a separate function.
(x-3)^2-2= x+1
⇓
f(x)= (x-3)^2-2, g(x)= x+1
Graphing the Functions
To find the points of intersection we will graph the functions. The x-coordinates are the solutions to the original equation. Pull out your graphing calculator, push Y=, and write the functions in the first two rows.
By pushing GRAPH the calculator will draw the functions in a coordinate plane.
Finding the Intersections
To find the points of intersection, push 2nd and then TRACE. This opens a menu where we choose intersect.
Having picked intersect, choose the first and second curve and pick a best guess for the point of intersection. After accepting the three questions, the coordinates of the intersection will be shown at the bottom.
Since we are only interested in the x-values, the solution to the equation is x=1. To find the second solution we repeat the procedure, but this time placing the cursor closer to the second point of intersection.
The second solution is x=6
Alternative Solution
Second Approach
We can also choose to solve the equations by moving all of the terms to one side of the equation.
(x-3)^2-2=x+1
⇕
(x-3)^2-x-3=0
With the new equation, we only have to graph one function and identify where it crosses the x-axis, which will be the zeros of the function. Let's use our graphing calculator again.
The zeros can now be found by pushing 2nd and then TRACE. A menu will appear where we should choose the option zero.
Having picked zero, choose the left-bound and right-bound such that this interval includes the zero we wish to calculate.
The first zero is x=1. To find the second zero, we will repeat the process but making sure that the boundaries includes the second zero.
