A cell phone company dropped the
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Answer:
B) Vertex (1,2), maximum
Step-by-step explanation:
First, determine if the graph has a maximum or a minimum value. Since the graph opens downwards, it has a <u>maximum</u> value.
The maximum is the point that has the greatest y value. We can see that the greatest y value is at . Going down two units from that spot, we can see that the x value is at
. We can plug those into the vertex form,
. By plugging in we get the point
.
If one of our zeros is 4, then the factor is x-4. If the second zero is 5i, then the conjugate root theorem says there HAS to be a root that is -5i. So our 3 factors are (x-4)(x+5i)(x-5i). We will FOIL out these factors to get the polynomial. Let's start with the ones that contain the imaginary numbers. Doing that mutliplication we get x^2-25i^2. i^2 is equal to -1, so what that expression simplifies down to is 
. Now we will multiply in that last factor of (x-4): 
. FOILing out we have 
. There you go!