Question
Suppose \( f(x)=2 x^{2}+5 x-3 \). Compute the following: A.) \( f(-5)+f(5)=\square \) B.) \( f(-5)-f(5)=\square \) Question Help: \( \square \) Video Submit Question
Ask by Bond Munoz. in the United States
Jan 27,2025
Real Tutor Solution
Tutor-Verified Answer
Answer
A.) \( f(-5) + f(5) = 94 \)
B.) \( f(-5) - f(5) = -50 \)
Solution
Sure, let's compute each part step by step.
Given the function:
\[ f(x) = 2x^{2} + 5x - 3 \]
### A.) Compute \( f(-5) + f(5) \)
1. **Calculate \( f(-5) \):**
\[
f(-5) = 2(-5)^2 + 5(-5) - 3 = 2(25) - 25 - 3 = 50 - 25 - 3 = 22
\]
2. **Calculate \( f(5) \):**
\[
f(5) = 2(5)^2 + 5(5) - 3 = 2(25) + 25 - 3 = 50 + 25 - 3 = 72
\]
3. **Add the two results:**
\[
f(-5) + f(5) = 22 + 72 = 94
\]
**Answer for Part A:** \( 94 \)
---
### B.) Compute \( f(-5) - f(5) \)
Using the previously calculated values:
\[
f(-5) - f(5) = 22 - 72 = -50
\]
**Answer for Part B:** \( -50 \)
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Simplify this solution Bonus Knowledge
To find \( f(-5) \) and \( f(5) \), we plug in the values into the function \( f(x) = 2x^2 + 5x - 3 \). First, calculate \( f(-5) \): \[ f(-5) = 2(-5)^2 + 5(-5) - 3 = 2 \cdot 25 - 25 - 3 = 50 - 25 - 3 = 22 \] Next, calculate \( f(5) \): \[ f(5) = 2(5)^2 + 5(5) - 3 = 2 \cdot 25 + 25 - 3 = 50 + 25 - 3 = 72 \] Now, for part A: \[ f(-5) + f(5) = 22 + 72 = 94 \] For part B: \[ f(-5) - f(5) = 22 - 72 = -50 \] Therefore, the final answers are: A.) \( f(-5) + f(5) = 94 \) B.) \( f(-5) - f(5) = -50 \)
