The score for a video game is calculated using f(x) = 4.5x2 + 7x + 2, where x represents the levels completed. If Alex completes 50 levels, what will be his score? 
A.4,902
B.577
C.2,852
D.11,602

To find Alex's score, we need to use the given function \( f(x) = 4.5x^2 + 7x + 2 \) and substitute \( x = 50 \) into the function, since Alex completed 50 levels.

The calculation proceeds as follows:

1. **Substitute \( x = 50 \) into the function:**

   \[
   f(50) = 4.5(50)^2 + 7(50) + 2
   \]

2. **Calculate \( 50^2 \):**

   \[
   50^2 = 2500
   \]

3. **Multiply \( 4.5 \) by \( 2500 \):**

   \[
   4.5 \times 2500 = 11250
   \]

4. **Calculate \( 7 \times 50 \):**

   \[
   7 \times 50 = 350
   \]

5. **Add these results together:**

   \[
   11250 + 350 + 2 = 11602
   \]

So, Alex's score is \( \boxed{11602} \).

**The correct answer is D. 11,602.**

Would you like further details or have any questions? Here are some related questions you might find interesting:

1. What would Alex's score be if he completed 60 levels instead?
2. How does the score function change if the coefficient of \( x^2 \) changes to 5?
3. What is the minimum score Alex can achieve, assuming \( x \) must be a non-negative integer?
4. How does the rate of increase in the score change as more levels are completed?
5. What would be the effect on the score if the function were \( f(x) = 4.5x^2 + 7x - 2 \) instead?

**Tip:** When dealing with quadratic functions like \( f(x) = ax^2 + bx + c \), remember that the term \( ax^2 \) has the most significant impact on the output as \( x \) gets larger.

Learn how to calculate a score using the quadratic function f(x) = 4.5x^2 + 7x + 2, with an example problem where Alex completes 50 levels. Follow the step-by-step solution to find out Alex's score and explore related questions about varying parameters of the function.

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