Use the factored form of a cubic equation, f(x)=a(x-p)(x-q)(x-r), where p, q, and r are the x-intercepts.
f(x)=(x+1)(x-1)(x-2)
Practice makes perfect
Using the general form of a factored cubic equation, we can write the factored form of the cubic function that passes through the given points.
f(x)=a(x-p)(x-q)(x-r)
In the above equation, p, q, and r are the x-intercepts of the function. We are told that the points ( - 1,0), (1,0), and (2,0) lie on the graph. Therefore, - 1, 1, and 2 are roots of the equation.
f(x)=a(x-( - 1))(x-1)(x-2)
⇕
f(x)=a(x+1)(x-1)(x-2)
Finally, we will find the value of a using the fact that the curve also passes through the point (0,2). We can substitute 0 for x and 2 for f(x) in our equation with the roots.
