Question

1. We know these things about a polynomial function, f(x): it has exactly one relative
maximum and one relative minimum, it has exactly three zeros, and it has a known
factor of (x - 4). Sketch a graph of f(x) given this information.

Answer 1

Answer:

Here's what I get  

Step-by-step explanation:

If the function has three zeros with one relative maximum and one relative minimum, it could be a cubic equation.

If it has a factor of x - 4, the graph crosses the x-axis at (4,0).

Your graph might look like the one below.

It has three zeros, one of which is at x = 4, and a local maximum and minimum.

Answer 2

We want to graph a polynomial with the given information.

The graph can be seen at the end of the answer.

We know that:

The polynomial has one minimum and one maximum.

The polynomial has 3 zeros, so it intercepts the x-axis at 3 points.

The factor (x - 4) is a factor of the polynomial, meaning that x = 4 is one of the zeros.

Then we can sketch a general graph, where you can see one relative maximum (at the right) and one relative minimum (at the left).

Also the 3 zeros, one particularly at x = 4.

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