**Answer:**

3

**Step-by-step explanation:**

f(x) = 4x^3 – 13x^2 + 9x + 2

This looks complicated but all we need to find are the Roots

We are looking for when y=0

So given each part of the information, we can label how many times it happens

The function starts from the bottom of quadrant 3: Starts lower left

and goes up through the x-axis at (0, negative 0.25) : This is ONE ROOT

and then through the y-axis at (0, 2). : It's now on the 2nd quartile

It then starts to curve down at (0.5, 4): It's moving towards y=0

until it reaches (1.75, negative 0.5).: It has now passed y=o and there are TWO ROOTS

It then curves up and crosses the x-axis at (2, 0) and goes up approaching x = 3: It has passed y=0 again, so there are THREE ROOTS

This polynomial function has 3 ROOTS