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Let’s analyze the given problem, where you are asked to sketch the graphs of parabolas based on the provided characteristics for each part.

### Part (a):
1. **Range**: \( y \leq 5 \), \( y \in \mathbb{R} \).  
   This tells us the maximum \( y \)-value of the parabola is 5, and the parabola opens downward.
   
2. **Axis of symmetry**: \( x = -2 \).  
   The parabola is symmetric about the line \( x = -2 \).
   
3. **y-intercept**: \( (0, 1) \).  
   The parabola crosses the y-axis at the point \( (0, 1) \).

   ### To sketch this:
   - Since the axis of symmetry is at \( x = -2 \), the vertex will be along this line.
   - The maximum point (vertex) should be at \( y = 5 \), on the line \( x = -2 \).
   - The parabola will pass through \( (0, 1) \), which lies 2 units to the right of the axis of symmetry.
   - Reflect this across the axis of symmetry to get another point at \( (-4, 1) \).

### Part (b):
1. **Range

Sketch the graph of a parabola for each set of characteristics given below. Show at least two other points on each graph. Part a) Range: {y | y ≤ 5, y ∈ R}, Axis of symmetry: x = -2, y-intercept: (0, 1). Part b) Range: {y | y ≥ -4, y ∈ R}, x-intercepts: (-2, 0) and (6, 0), x-coordinate of vertex: 2

Learn how to sketch parabolas with given range, axis of symmetry, and intercepts. Understand the algebraic concepts and the use of quadratic equations in graphing parabolas. Suitable for high school students in Grades 9-11.

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