Question #6453213Fill 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. It requires the student to determine the minimum value of the polynomial and use it to find the range.
This question tests the understanding of the range of an even-degree polynomial. It requires the student to determine the minimum value of the polynomial and use it to find the range.
Key Concept Explanation
For even-degree polynomials with a positive leading coefficient, the range is , where is the minimum value of the polynomial.
For even-degree polynomials with a positive leading coefficient, the range is , where is the minimum value of the polynomial.
Step-by-step Solution
1. Identify the given polynomial:
2. Recognize that this is an even-degree polynomial with a positive leading coefficient.
3. Complete the square to find the minimum value:
1. Identify the given polynomial:
2. Recognize that this is an even-degree polynomial with a positive leading coefficient.
3. Complete the square to find the minimum value:
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