We are given a few statements that describe a quartic function and one that does not. Let's try to provide an example for each option given about a quartic function.
The End Behavior of the Function is Up and Up
Let's graph a quartic function that has and up and up end behavior.
As we can see from the graph, the end behavior can be up and up.
The Function Has 4 Zeros
The real zeros of a function are the x-intercepts of its graph. We will graph a quartic function that has 4 zeros.
Looking at the graph, we can conclude that the function can have four zeros.
The Function Has 4 Turning Points
Let's try to graph a quartic function with 4 turning points.
The graph of a polynomial function of degree 4 can have at most 3 turning points. Therefore, the statement is never true.
The Function Has Complex Roots
A quartic function has always four roots. We will try to graph a quartic function that has two real roots. This would mean that its other two roots are complex.
This statement can also be true.
Conclusion
We found that a quartic function can never have four turning points. This corresponds to statement H.
