# HiSET: Math : Use the zeros to construct a rough graph of a function

## Example Questions

### Example Question #1 : Zeroes Of Polynomials

The graph of a function is shown below, with labels on the y-axis hidden.

Determine which of the following functions best fits the graph above.

Explanation:

Use the zeroes of the graph to determine the matching function. Zeroes are values of x where . In other words, they are points on the graph where the curve touches zero.

Visually, you can see that the curve crosses the x-axis when , and . Therefore, you need to look for a function that will equal zero at these x values.

A function with a factor of  will equal zero when  , because the factor of  will equal zero. The matching factors for the other two zeroes,  and , are  and , respectively.

The answer choice  has all of these factors, but it is not the answer because it has an additional zero that would be visible on the graph. Notice it has a factor of , which results in a zero at . This additional zero that isn't present in the graph indicates that this cannot be matching function.

is the answer because it has all of the required factors and, as a result, the required zeroes, while not having additional zeroes. Notice that the constant coefficient of negative 2 does not affect where the zeroes are.

### Example Question #2 : Zeroes Of Polynomials

Which of the functions below best matches the graphed function?