Answer:
2
Explanation:
You want the least possible degree of the polynomial graphed in the given figure.
Degree
There are several ways to determine the degree of the polynomial in the graph.
1. The degree is at least the maximum number of times a horizontal line will intersect the curve.
Here, there are two x-intercepts, so the degree is at least 2.
2. The degree is at least one more than the number of turning points. Here, there is one turning point (near (0.5, 1)), so the degree is at least 1+1 = 2.
3. The degree is at least 2 more than the number of times the concavity changes sign.
Here the curve is concave downward, and does not change concavity. The degree is at least 0 +2 = 2.
The least possible degree of the graphed polynomial is 2.
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Additional comment
You will recognize the graph is of a quadratic function, degree 2.
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