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)=1/7(x+5)(x-1)(x-4)
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 ( - 5,0), (1,0), and (4,0) lie on the graph. Therefore, - 5, 1, and 4 are roots of the equation.
f(x)=a(x-( - 5))(x-1)(x-4)
⇕
f(x)=a(x+5)(x-1)(x-4)
Finally, we will find the value of a using the fact that the curve also passes through the point (2,- 2). We can substitute 2 for x and - 2 for f(x) in our equation with the roots.
