Suppose f(x)=-x2+x-9. Compute the following:
f(-2)+f(4)=

We are given the function \( f(x) = -x^2 + x - 9 \) and asked to compute \( f(-2) + f(4) \).

### Step 1: Calculate \( f(-2) \)

Substitute \( x = -2 \) into the function \( f(x) \):

\[
f(-2) = -(-2)^2 + (-2) - 9
\]

\[
f(-2) = -(4) - 2 - 9 = -4 - 2 - 9 = -15
\]

### Step 2: Calculate \( f(4) \)

Substitute \( x = 4 \) into the function \( f(x) \):

\[
f(4) = -(4)^2 + 4 - 9
\]

\[
f(4) = -(16) + 4 - 9 = -16 + 4 - 9 = -21
\]

### Step 3: Add \( f(-2) \) and \( f(4) \)

Now, add the two results together:

\[
f(-2) + f(4) = -15 + (-21) = -36
\]

Thus, \( f(-2) + f(4) = -36 \).

Would you like further details or clarifications on any step?

Here are some related questions:
1. How do we find the roots of the quadratic function \( f(x) = -x^2 + x - 9 \)?
2. What is the vertex of the function \( f(x) = -x^2 + x - 9 \)?
3. How would you sketch the graph of \( f(x) = -x^2 + x - 9 \)?
4. What is the maximum or minimum value of \( f(x) = -x^2 + x - 9 \)?
5. How does changing the coefficient of \( x^2 \) affect the graph of the function?

**Tip**: The vertex form of a quadratic function can give you insights into the direction of the parabola and its maximum or minimum value.

Suppose f(x)=-x^2+x-9. Compute the following: f(-2)+f(4)=

Learn how to evaluate f(-2) and f(4) for the quadratic function f(x) = -x^2 + x - 9. This step-by-step solution covers key algebraic concepts related to quadratic functions and function evaluation, suitable for students in Grades 9-10.

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