Question #6453205Fill in the Blank
Algebra-1
Question
The range of the polynomial is __________.
Answer & Analysis
Analysis
Question Analysis
This question tests the understanding of the range of an even-degree polynomial with a negative leading coefficient.
This question tests the understanding of the range of an even-degree polynomial with a negative leading coefficient.
Key Concept Explanation
For even-degree polynomials, the range depends on the leading coefficient. A negative leading coefficient means the graph opens downwards, and the range is , where is the maximum value.
For even-degree polynomials, the range depends on the leading coefficient. A negative leading coefficient means the graph opens downwards, and the range is , where is the maximum value.
Step-by-step Solution
1. Substitute :
Since , becomes , where .
2. Find the vertex of :
For , , . The vertex (maximum point, since ) occurs at:
1. Substitute :
Since , becomes , where .
2. Find the vertex of :
For , , . The vertex (maximum point, since ) occurs at:
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