123k views
1 vote
Let the graph of f(x) be given below. Find the formula of f(x), a polynomial function, of least degree.

Let the graph of f(x) be given below. Find the formula of f(x), a polynomial function-example-1

1 Answer

2 votes

f(x)\text{ = }(1)/(2)x(x\text{ }+2)(x-4)

Step-by-step explanation:

To detrmine the formula of the polynomial, we check for the roots on the graph:

when y = 0, x = -2

when y = 0, x = 4

We have two roots.

x = -2

x + 2 = 0

x = 4

x - 4 = 0

3rd factor is x = 0

Hence, we have two factors: x(x + 2) and (x - 4)

The polynomial function using the factors:


f(x)\text{ = ax(x + 2)(x - 4)}

Next, we find the value of a:

To get a , we pick a point on the graph. let the point be (0, -4)

substitute the point in the function above:


\begin{gathered} f(x)\text{ = y = -4, x = 0} \\ -4\text{ = a(0 + 2) (0 - 4)} \\ -4\text{ = a(2)(-4)} \\ -4\text{ = -8a} \\ a\text{ = -4/-8} \\ a\text{ = 1/2} \end{gathered}

The formula of the polynomial becomes:


f(x)\text{ = }(1)/(2)x(x\text{ }+2)(x-4)

User Bjarni Ragnarsson
by
8.2k points

No related questions found

Welcome to QAmmunity.org, where you can ask questions and receive answers from other members of our community.

9.4m questions

12.2m answers

Categories