Question

A quartic function has zeros at -1, -3, and 5 (order 2) and a y-intercept of 150. Determine the equation of this function

a) f(x)=(x+1)2(x+3)2(x−5)
b) f(x)=(x−1)2(x−3)2(x+5)
c) f(x)=(x+1)(x+3)(x−5)
d) f(x)=(x−1)(x−3)(x+5)

Answer 1

The equation of the quartic function with zeros at -1, -3 (order 2), and 5, and a y-intercept of 150 is f(x) = (x+1)^2(x+3)^2(x-5).

Step-by-step explanation:

The equation of the quartic function with zeros at -1, -3 (order 2), and 5, and a y-intercept of 150 can be determined by using the zero product property. The zeros can be written as (x+1)(x+1)(x+3)(x+3)(x-5), since the zeros at -1 and -3 have an order of 2. Multiplying these factors together, we get f(x) = (x+1)2(x+3)2(x-5).

Therefore, option a) f(x) = (x+1)2(x+3)2(x-5) is the correct equation of the quartic function.