Question

Write a polynomial equation that, when graphed, would create three evenly peaked hills.

A. f(x) = (x + 2)² * (x - 1)² * (x - 4)²
B. f(x) = (x + 2)³ * (x - 1)³ * (x - 4)³
C. f(x) = (x + 2)⁴ * (x - 1)⁴ * (x - 4)⁴
D. f(x) = (x + 2)⁵ * (x - 1)⁵ * (x - 4)⁵

Answer 1

The polynomial equation that would create three evenly peaked hills is A. f(x) = (x + 2)² * (x - 1)² * (x - 4)² due to the even exponents and distinct zeros.

Step-by-step explanation:

The correct polynomial equation that creates three evenly peaked hills when graphed is f(x) = (x + 2)² * (x - 1)² * (x - 4)². To achieve this, the equation must have factors with even exponents, which create the hills, and distinct zeros to ensure that the hills are evenly spaced out. The given equation will have zeros at x = -2, x = 1, and x = 4, with each zero being a turning point because of the square term that ensures a hill shape at each zero. So, the correct answer is A. f(x) = (x + 2)² * (x - 1)² * (x - 4)².