The score for a video game is calculated using *f(x)* = 4.5*x*2 + 7*x* + 2, where *x* represents the levels completed. If Alex completes 50 levels, what will be his score? 

A.577

B.4,902

C.2,852

D.11,602


To find Alex's score after completing 50 levels, we need to evaluate the function \( f(x) = 4.5x^2 + 7x + 2 \) at \( x = 50 \).

Substituting \( x = 50 \):

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

Let's calculate this step-by-step:

1. Calculate \( 50^2 \).
2. Multiply the result by 4.5.
3. Multiply 50 by 7.
4. Add all the values together.

Let's perform the calculations: 

\[
f(50) = 4.5 \times 2500 + 7 \times 50 + 2
\]

\[
= 11250 + 350 + 2
\]

\[
= 11,602
\]

So, the correct answer is:

**D. 11,602**

Would you like a more detailed explanation, or do you have any questions?

### Related Questions:
1. How would the score change if the coefficient of \(x^2\) was different?
2. What would Alex’s score be if he completed 100 levels?
3. How does increasing the coefficient of \(x\) affect the overall score?
4. If the function were \(f(x) = 5x^2 + 6x + 3\), what would be the score for completing 50 levels?
5. How can you determine the average score increase per level?

**Tip:** Always plug in values carefully to avoid calculation errors, especially with quadratic functions!

Find out Alex's video game score after completing 50 levels using the quadratic function f(x) = 4.5x^2 + 7x + 2. Follow a step-by-step solution with detailed calculations and learn about quadratic equations and function evaluation. Suitable for high school students.

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