Question
Given \( f(x)=-x^{2}+4 x+10 \), find \( f(-6) \)
Ask by Ryan Daniels. in the United States
Jan 24,2025
Real Tutor Solution
Tutor-Verified Answer
Answer
\( f(-6) = -50 \)
Solution
To find \( f(-6) \) for the function \( f(x) = -x^2 + 4x + 10 \), follow these steps:
1. **Substitute \( x = -6 \) into the function:**
\[
f(-6) = -(-6)^2 + 4(-6) + 10
\]
2. **Calculate \( (-6)^2 \):**
\[
(-6)^2 = 36
\]
So,
\[
f(-6) = -36 + 4(-6) + 10
\]
3. **Multiply \( 4 \) by \( -6 \):**
\[
4(-6) = -24
\]
Now, the expression becomes:
\[
f(-6) = -36 - 24 + 10
\]
4. **Combine the terms:**
\[
-36 - 24 = -60
\]
\[
-60 + 10 = -50
\]
**Therefore, \( f(-6) = -50 \).**
**Answer:** \(-50\)
Reviewed and approved by the UpStudy tutoring team
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Simplify this solution Beyond the Answer
To find \( f(-6) \), we need to substitute \(-6\) into the function \( f(x) \). \[ f(-6) = -(-6)^2 + 4(-6) + 10 \] Calculating each term step by step: 1. \( -(-6)^2 = -36 \) (since \((-6)^2 = 36\)) 2. \( 4(-6) = -24 \) 3. Combining these: \[ f(-6) = -36 - 24 + 10 \] Now, simplify: \[ f(-6) = -36 - 24 + 10 = -36 - 24 = -60 + 10 = -50 \] Thus, \( f(-6) = -50 \).
