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Determine which statement is true about the zeros of the function graphed below.
An upward parabola f on a coordinate plane vertex at (1, 4) and intercepts the y-axis at 5 units.

A.
Function f has exactly two complex solutions.
B.
Function f has exactly one real solution and no complex solutions.
C.
Function f has exactly two real solutions.
D.
Function f has one real solution and one complex solution.

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sqdancefan

Answer:

  A.  Function f has exactly two complex solutions.

Step-by-step explanation:

The function will have real solutions where the graph crosses the x-axis. It will always have a total number of solutions equal to its degree. The ones that are not real are complex.

Application

The graph has its vertex above the x-axis and extends upward from there. It never crosses the x-axis, so there are no real solutions. That means both solutions are complex.

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