Graphs of Polynomial Functions

Question

2

Given the function :

its -intercept is 

its -intercepts are

Answer 1

To find the intercepts, we will first factor out f(n)

f(n) = 2n⁴ - 26n³ + 84n²

f(n) = 2n²(n² - 13n + 42)

f(n) = 2n²(n-6)(n-7)

Looking at our factored form of f(n), we can determine that the n-intercepts are 0, 6, and 7 because f(n) = 0 when n = 0, 6, 7

We can also determine that the f-intercept is 0 because when n = 0, f(n) = 0