Algebra-1

Question Analysis
This question involves finding the range of the quadratic polynomial . The main focus is on analyzing the quadratic’s vertex (to find its minimum value) and its end behavior (to confirm no upper bound).

Key Concept Explanation
Quadratic Function Form: A quadratic has a parabola as its graph. If , the parabola opens upward, with a minimum value at its vertex (no maximum, as it extends to ).
Vertex Formula: The x-coordinate of the vertex is ; substitute this into the quadratic to find the minimum y-value (the lower bound of the range).

Step-by-step Solution
1. Identify :
For , (positive, so opens upward), , .
2. Find the vertex’s x-coordinate:
Use .
3. Calculate the minimum value (vertex’s y-coordinate):
Substitute

Click "Show Answer" to reveal the answer and analysis