Answer:
- f(x) = 1/18(x + 2)(x - 1)²(x - 3)³
Step-by-step explanation:
Analyzing the graph:
- It's even degree as overall U-shaped
- Zeros at -2, 1, 3. It gives us factors of (x + 2), (x - 1) and (x - 3)
- Touches the x-axis at x = 1, its indication of (x - 1) is of degree 2.
- Touches and intersects the x- axis at x = 3, its indication of (x - 3) is degree 3.
According to the above observations we have:
- f(x) = a(x + 2)(x - 1)²(x - 3)³
Since we don't see the exact minimum of function we assume a = 1/18 is approximately what we need.
So the equation is:
- f(x) = 1/18(x + 2)(x - 1)²(x - 3)³
See attached graph
