given that f(x) is a degree 3 polynomial with zeros at -8, 1, 6, find an equation for f(x) given that f(-4) = 7.

First we know f(x) is a 3rd degree polynomial => it has the following form.

There is however a very famous theorem, namely ''The fundamental Theorem of Algebra'' which states that any polynomial equation of degree n, has n roots/zeroes in the real and imaginary set.

But we also know if r is a root of a polynomial than the binomial (x-r) is a factor of the original equation, these 2 statements combined give rise to the following:

Using the following means that in your problem the polynomial is constructed by taking the product of the linear factors / (x-r) where r are the roots. One such factor for each root which yields:

boxplot e is the answer

  the correct choice is marked

step-by-step explanation:

the first two graphs show multiple turning points. the last graphs matches the description in every detail.