Given ​f(x)equals2x squaredplus 2xplus 6​, find ​f(negative 6​).

Question

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Part 1
A.66
66
B.60
60
C.80
80
D.negative 18
negative 18

Answer 1

To find \( f(-6) \) for the function \( f(x) = 2x^2 + 2x + 6 \), we substitute \(-6\) for \(x\):

\[ f(-6) = 2(-6)^2 + 2(-6) + 6 \]

Now, calculate each term step-by-step:

1. Calculate \((-6)^2\): \[ (-6)^2 = 36 \]

2. Multiply by 2: \[ 2 \times 36 = 72 \]

3. Calculate \(2(-6)\): \[ 2 \times -6 = -12 \]

4. Add it all together: \[ f(-6) = 72 - 12 + 6 \]

5. Combine the terms: \[ 72 - 12 = 60 \] \[ 60 + 6 = 66 \]

Thus, \( f(-6) = 66 \).

The answer is A. 66.