Question #6453209Fill 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 positive leading coefficient. The range of such a polynomial is , where is the minimum value of the function.
This question tests the understanding of the range of an even-degree polynomial with a positive leading coefficient. The range of such a polynomial is , where is the minimum value of the function.
Key Concept Explanation
For even-degree polynomials with a positive leading coefficient, the graph opens upwards, and the range is from the minimum value to infinity.
For even-degree polynomials with a positive leading coefficient, the graph opens upwards, and the range is from the minimum value to infinity.
Step-by-step Solution
1. Substitute :
Since , becomes , where .
2. Find the vertex of :
For , , . The vertex (minimum point, since ) occurs at: .
1. Substitute :
Since , becomes , where .
2. Find the vertex of :
For , , . The vertex (minimum point, since ) occurs at: .
Want More Practice Questions?
Access thousands of practice questions with detailed explanations on Scholardog.
Practice Now - It's Free!