Question
Which graph represents the polynomial function h(x)=x^3+2x^2-11x-12
Solution
4.2
(251 Votes)
Colette
Master ยท Tutor for 5 years
Answer
### The graph that passes through the points
,
, and
, and has the described end behavior. You would need to be provided with graph options to select the correct one.
Explanation
## Step 1: Find the roots of the polynomial### To graph the polynomial, we first need to find its roots (x-intercepts). We can do this by factoring or using numerical methods. Since the polynomial is
, we can try integer factors of -12. We find that
,
, and
. Therefore, the roots are
,
, and
.## Step 2: Determine the end behavior### As the leading term is
, the end behavior of the graph is as follows: as
,
, and as
,
.## Step 3: Sketch the graph### Using the roots and the end behavior, we can sketch the graph. The graph passes through the x-axis at
,
, and
. It rises to the right and falls to the left.