Question

select the correct answer.
the zeros of a quadratic function are 6 and -4. which of these choices could be the function?
a. ( f(x) = (x - 6)(x - 4) )
b. ( f(x) = (x - 6)(x + 4) )
c. ( f(x) = (x + 6)(x - 4) )
d. ( f(x) = (x + 6)(x + 4) )

Explanation:

Step1: Recall zero - factor property

If a quadratic function has zeros at \(x = a\) and \(x=b\), then the factored form of the quadratic function is \(f(x)=(x - a)(x - b)\).

Step2: Determine the factors from zeros

Given that the zeros of the quadratic function are \(x = 6\) and \(x=- 4\).
For the zero \(x = 6\), the corresponding factor is \((x - 6)\) (because if \(x-6=0\), then \(x = 6\)).
For the zero \(x=-4\), we can rewrite \(x=-4\) as \(x + 4=0\), so the corresponding factor is \((x + 4)\).

Step3: Write the function

Using the factored form of a quadratic function with zeros \(a = 6\) and \(b=-4\), the function is \(f(x)=(x - 6)(x + 4)\).

Answer:

B. \(f(x)=(x - 6)(x + 4)\)