The graph of a second-order polynomial is shown below, and the intercepts with the axes are marked. Explain how you can use the graph to write the polynomial as a product of linear factors (x-a)(x-b). Be sure to state the values of a and b.
...is shown below...
To write a second-order polynomial as a product of linear factors in the form (x-a)(x-b), we are essentially looking for the values of a and b that correspond to the x-intercepts of the graph.
In this case, the x-intercepts are the points where the graph intersects the x-axis. Let's call these points A and B. Point A has an x-coordinate of a, and point B has an x-coordinate of b.
To find the values of a and b, we can visually inspect the graph and observe where it crosses the x-axis. The points at which it crosses the x-axis are the intercepts.
Once we have identified the intercepts, we can write the polynomial as a product of linear factors. Since the graph has intercepts at points A and B, we can write the polynomial as (x-a)(x-b) by replacing a and b with the corresponding x-coordinates of the intercepts.
To summarize, to write the second-order polynomial as a product of linear factors (x-a)(x-b), we need to find the x-intercepts on the graph, which correspond to the values of a and b.