Question #6453196Fill 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 and the vertex of the graph. A negative leading coefficient means the graph opens downwards, and the range is from negative infinity to the maximum value.
For even-degree polynomials, the range depends on the leading coefficient and the vertex of the graph. A negative leading coefficient means the graph opens downwards, and the range is from negative infinity to the maximum value.
Step-by-step Solution
1. Substitute : Since , . The polynomial becomes .
2. Find maximum of : For , , so maximum at
1. Substitute : Since , . The polynomial becomes .
2. Find maximum of : For , , so maximum at
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