Questions: Given f(x)=-3x^2-x-15, find f(-8)

Transcript text: Given $f(x)=-3 x^{2}-x-15$, find $f(-8)$

Solution

To evaluate the quadratic function $ f(x) = -3x^2 - x - 15 $ at $ x = -8 $, substitute $-8$ for $ x $ in the function and compute the result.

Step 1: Substitute $ x = -8 $ into the function

We start with the quadratic function given by

\[ f(x) = -3x^2 - x - 15 \]

To find $ f(-8) $, we substitute $-8$ for $ x $:

\[ f(-8) = -3(-8)^2 - (-8) - 15 \]

Step 2: Calculate $ (-8)^2 $

Calculating the square of $-8$:

\[ (-8)^2 = 64 \]

Step 3: Substitute and simplify

Now we substitute $ 64 $ back into the function:

\[ f(-8) = -3(64) + 8 - 15 \]

Step 4: Perform the multiplications and additions

Calculating each term:

\[ -3(64) = -192 \]

Now, substituting this value into the equation:

\[ f(-8) = -192 + 8 - 15 \]

Step 5: Combine the results

Now we combine the results:

\[ f(-8) = -192 + 8 = -184 \] \[ f(-8) = -184 - 15 = -199 \]

Thus, the value of $ f(-8) $ is

\[ \boxed{-199} \]

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