Question

writing the equation of polynomial functions
determine the roots of the function
what are the 4 roots here?
(-3,0) (-1,0) (1,0) (2,0)
(-2,0) (-1,0) (1,0) (2,0)
rewatch

Explanation:

Step1: Identify x-intercepts

The roots of a polynomial function are the x - intercepts (where the graph crosses or touches the x - axis). From the graph, we look for the points where the blue graph intersects the x - axis.

Step2: Determine the x - values

Looking at the x - axis markings, the intersection points (roots) seem to be at \(x=-2\), \(x = - 1\), \(x=1\), and \(x = 2\)? Wait, no, wait. Wait, maybe I misread. Wait, looking at the options, the first set of options: (-2,0), (-1,0), (1,0), (2,0)? Wait, no, the lower part: the first column of checkboxes: (-3,0), (-1,0), (1,0), (2,0) and the second: (-2,0), (-1,0), (1,0), (2,0). Wait, from the graph (the blue graph), the x - intercepts (roots) are the points where y = 0. Looking at the graph, the intersections are at x=-2, x=-1, x = 1, x = 2? Wait, no, maybe the graph has roots at (-2,0), (-1,0), (1,0), (2,0)? Wait, let's check the options. The second set of checkboxes (the one with (-2,0), (-1,0), (1,0), (2,0)): those are the roots. Because the roots of a polynomial are the x - values where the function equals zero, i.e., the x - intercepts. So we identify the x - intercepts from the graph.

Answer:

The roots (x - intercepts) of the function are the points where the graph crosses the x - axis. From the graph, the roots are \((-2,0)\), \((-1,0)\), \((1,0)\), \((2,0)\). So the correct options (the checkboxes to mark) are \(\boldsymbol{(-2,0)}\), \(\boldsymbol{(-1,0)}\), \(\boldsymbol{(1,0)}\), \(\boldsymbol{(2,0)}\) (the second set of checkboxes with these points).