Replace 0 with y to obtain the associated function. Then, graph this function and identify the x-intercepts.
(x+2)(x-1)(x-4)
Practice makes perfect
The given equation is already written in standard form. Therefore, to solve by graphing, we will graph the associated function. To obtain it, we will replace 0 with y.
Equation:& x^3-3x^2-6x+8=0
Function:& y=x^3-3x^2-6x+8
Now, we can enter the function in the calculator by pushing Y= and writing the function rule.
Next, by pushing GRAPH, the calculator will draw the graph of the equation. Note that we are looking for x-values that make the y-value equal 0. This means that we are looking for the x-intercepts of the graph.
We can see that the graph intersects the x-axis at three different places. Therefore, the equation has three solutions. To find them, we can use the zero option in the calculator. This can be done by pressing 2ND and then CALC.
After selecting the "zero" option, we need to choose left and right boundaries for each of the zeros. Finally, the calculator asks for a guess where the zero might be. After that, it will calculate the exact point for us. We will have to do this three times, once for each zero.
This equation's solutions are x= - 2, x= 1, and x= 4. Let's use this information to write the non-zero side of the equation.
(x-( - 2))(x- 1)(x- 4)
⇕
(x+2)(x-1)(x-4)
