Graphical Behavior
Looking for Patterns
Example 2
Graph the polynomial p(x) = (-x + 2)(x2 + 5).
Step 1. Plot the real roots.
Set each factor equal to zero to find the roots.
Therefore, there is only one real root and that is x = 2.
Step 2. Use the leading coefficient to determine the end behavior.
Multiply the polynomial to get -x3 + 2x2 - 5x + 10 or (-x)(x2) to find that the leading coefficient is -1.
Therefore the graph goes from upper left to lower right.
Step 3. Substitute the value x = 0, find the value of y.
This calculation produces the point (0, 10).
Combining this bit of information, the sketch of the graph could look like:
*Note: With the information given, it is not possible to determine the exact shape of the graph. This graph is an approximation.