Which statement describes the graph of this polynomial function?

Question

f(x)=x⁵-6x⁴+9x³

1. The graph crosses the x axis at x = 0 and touches the x axis at x = 3.
2. The graph touches the x axis at x = 0 and crosses the x axis at x = 3.
3. The graph crosses the x axis at x = 0 and touches the x axis at x = –3.
4. The graph touches the x axis at x = 0 and crosses the x axis at x = –3.

Answer 1

Here are the simplest functions for each option:

 

1. x(x-3)² = x³ - 6x² + 9x
2. x²(x-3) = x³ - 3x²
3. x(x+3)² = x³ + 6x² + 9x
4. x²(x+3) = x³ + 3x²

 

One of them should correspond to the function in your problem (which you didn't state).