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+3)(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 ( - 3,0), (- 1,0), and (2,0) lie on the graph. Therefore, - 3, - 1, and 2 are roots of the equation.
f(x)=a(x-( - 3))(x-(- 1))(x-2)
⇕
f(x)=a(x+3)(x+1)(x-2)
Finally, we will find the value of a using the fact that the curve also passes through the point (- 2,4). We can substitute - 2 for x and 4 for f(x) in our equation with the roots.
