The given function is $f(x) = -2x^2 - x + 1$. You are asked to compute:

A) $f(-5) + f(4)$

We need to first calculate $f(-5)$ and $f(4)$.

1. For $f(-5)$: $f(-5) = -2(-5)^2 - (-5) + 1$ $= -2(25) + 5 + 1$ $= -50 + 5 + 1 = -44$

2. For $f(4)$: $f(4) = -2(4)^2 - 4 + 1$ $= -2(16) - 4 + 1$ $= -32 - 4 + 1 = -35$

Now, sum them up: $f(-5) + f(4) = -44 + (-35) = -79$

B) $f(-5) - f(4)$

We already know $f(-5) = -44$ and $f(4) = -35$.

So: $f(-5) - f(4) = -44 - (-35) = -44 + 35 = -9$

Final Answers:

• A) $f(-5) + f(4) = -79$
• B) $f(-5) - f(4) = -9$

Would you like more details or have any other questions?

Here are five related questions:

1. How do you find the roots of the quadratic equation $f(x) = 0$?
2. What is the vertex of the quadratic function $f(x) = -2x^2 - x + 1$?
3. How do you determine whether $f(x)$ has a maximum or a minimum value?
4. What is the domain and range of $f(x) = -2x^2 - x + 1$?
5. How would you compute the value of $f(x)$ for any arbitrary $x$?

Tip: Always plug in values carefully when dealing with negative numbers, especially when squaring them.