Use either a graphing calculator or a spreadsheet to complete the table. Express all your answers as decimals rounded to four decimal places.
x	y	
f(x, y) = x2ey
0	1	  
Correct: Your answer is correct.
−3
2	  
Incorrect: Your answer is incorrect.
 
See the rounding prompt for how many decimal places are needed.
1.3	3.3	  
Incorrect: Your answer is incorrect.
9	8	  
Incorrect: Your answer is incorrect.


To solve the problem, we'll compute the values of the function \( f(x, y) = x^2 e^y \) for the given \( x \) and \( y \) values and then round them to four decimal places.

### Step-by-Step Calculations

1. **Compute \( f(x, y) \) for each pair of (x, y):**
   
   The formula is:
   \[
   f(x, y) = x^2 \cdot e^y
   \]
   where:
   - \( x \) is given.
   - \( y \) is given.
   - \( e \) is the mathematical constant approximately equal to 2.71828.

2. **Round each result to four decimal places.**

Let's compute the values:

1. \( x = -3, y = 2 \)
   \[
   f(-3, 2) = (-3)^2 \cdot e^2 = 9 \cdot e^2
   \]
   
2. \( x = 1.3, y = 3.3 \)
   \[
   f(1.3, 3.3) = (1.3)^2 \cdot e^{3.3} = 1.69 \cdot e^{3.3}
   \]

3. \( x = 9, y = 8 \)
   \[
   f(9, 8) = (9)^2 \cdot e^8 = 81 \cdot e^8
   \]

Now, let's compute these values.Here are the computed values of \( f(x, y) = x^2 e^y \) rounded to four decimal places for each pair of \( (x, y) \):

1. For \( x = -3, y = 2 \):
   \[
   f(-3, 2) \approx 66.5015
   \]

2. For \( x = 1.3, y = 3.3 \):
   \[
   f(1.3, 3.3) \approx 45.8204
   \]

3. For \( x = 9, y = 8 \):
   \[
   f(9, 8) \approx 241457.5970
   \]

Would you like any further details or explanations? 

### Related Questions:
1. How do you compute exponential functions using a graphing calculator?
2. Why is rounding to four decimal places important in mathematical computations?
3. How can we interpret the exponential growth in the function \( f(x, y) = x^2 e^y \)?
4. What are some real-world applications of exponential functions like \( f(x, y) = x^2 e^y \)?
5. How does changing \( x \) or \( y \) affect the value of \( f(x, y) \)?

**Tip:** Always double-check the values you input into your calculator or spreadsheet to ensure accuracy.

Use either a graphing calculator or a spreadsheet to complete the table. Express all your answers as decimals rounded to four decimal places.
x	y	
f(x, y) = x^2e^y
0	1	  
Correct: Your answer is correct.
−3	2	  
Incorrect: Your answer is incorrect.
See the rounding prompt for how many decimal places are needed.
1.3	3.3	  
Incorrect: Your answer is incorrect.
9	8	  
Incorrect: Your answer is incorrect.

Learn how to solve the function f(x, y) = x^2e^y using a graphing calculator or spreadsheet. This problem involves exponential and quadratic functions, requiring answers to be rounded to four decimal places. Explore the step-by-step process for solving this problem, suitable for Grades 10-12.

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