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)=1/6(x+6)(x+3)(x-3)
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 ( - 6,0), (- 3,0), and (3,0) lie on the graph. Therefore, - 6, - 3, and 3 are roots of the equation.
f(x)=a(x-( - 6))(x-(- 3))(x-3)
⇕
f(x)=a(x+6)(x+3)(x-3)
Finally, we will find the value of a using the fact that the curve also passes through the point (0,- 9). We can substitute 0 for x and - 9 for f(x) in our equation with the roots.
