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The problem asks for seven ordered pairs that satisfy the equation \( y = 3 - x^2 \), and then to determine the graph of the equation.

### Step 1: Find the Ordered Pairs
To find the ordered pairs, we substitute different values of \( x \) into the equation and calculate the corresponding values of \( y \).

Let's calculate \( y \) for a range of values of \( x \):

1. **When \( x = -3 \):**
   \[
   y = 3 - (-3)^2 = 3 - 9 = -6
   \]
   So, the ordered pair is \( (-3, -6) \).

2. **When \( x = -2 \):**
   \[
   y = 3 - (-2)^2 = 3 - 4 = -1
   \]
   So, the ordered pair is \( (-2, -1) \).

3. **When \( x = -1 \):**
   \[
   y = 3 - (-1)^2 = 3 - 1 = 2
   \]
   So, the ordered pair is \( (-1, 2) \).

4. **When \( x = 0 \):**
   \[
   y = 3 - 0^2 = 3 - 0 = 3
   \]
   So, the ordered pair is \( (0, 3) \).

5. **When \( x = 1 \):**
   \[
   y = 3 - 1^2 = 3 - 1 = 2
   \]
   So, the ordered pair is \( (1, 2) \).

6. **When \( x = 2 \):**
   \[
   y = 3 - 2^2 = 3 - 4 = -1
   \]
   So, the ordered pair is \( (2, -1) \).

7. **When \( x = 3 \):**
   \[
   y = 3 - 3^2 = 3 - 9 = -6
   \]
   So, the ordered pair is \( (3, -6) \).

### Summary of Ordered Pairs:
The seven ordered pairs are:
- \( (-3, -6) \)
- \( (-2, -1) \)
- \( (-1, 2) \)
- \( (0, 3) \)
- \( (1, 2) \)
- \( (2, -1) \)
- \( (3, -6) \)

### Step 2: Graph of the Equation
The graph of \( y = 3 - x^2 \) is a parabola that opens downwards with its vertex at \( (0, 3) \). The symmetry of the parabola is evident from the pairs, with the same \( y \)-values repeating symmetrically on both sides of \( x = 0 \).

Would you like a detailed graph or further explanation? 

### Related Questions:
1. What is the vertex form of the equation \( y = 3 - x^2 \)?
2. How would you determine the axis of symmetry for the graph?
3. What are the intercepts of the graph, and how are they found?
4. How does the value of the coefficient of \( x^2 \) affect the direction of the parabola?
5. How can you determine if a given point lies on the parabola \( y = 3 - x^2 \)?

### Tip:
When graphing quadratic functions, always identify the vertex and axis of symmetry first, as they help guide the shape of the graph.

Find seven ordered pairs that satisfy the equation y = 3 - x^2, and then determine its graph.

This problem involves finding seven ordered pairs for the equation y = 3 - x^2 and graphing the equation. Learn key algebraic concepts such as quadratic equations, symmetry, and graphing parabolas. Suitable for students in Grades 9-10.

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