Use the following function rule to find *f*(–4).



*f*(*x*)

 = 

2

*x*

 + 

2

*x*

2
 
 + 

10

*f*(–4) = 

To find \( f(-4) \), we will substitute \( x = -4 \) into the function rule for \( f(x) \):

\[
f(x) = 2x + 2x^2 + 10
\]

Now, substitute \( x = -4 \):

\[
f(-4) = 2(-4) + 2(-4)^2 + 10
\]

### Step-by-step calculation:
1. \( 2(-4) = -8 \)
2. \( (-4)^2 = 16 \), so \( 2(16) = 32 \)
3. Finally, add \( 10 \) to the result.

So,

\[
f(-4) = -8 + 32 + 10 = 34
\]

Thus, \( f(-4) = 34 \).

Would you like more details or have any questions?

Here are 5 related questions:
1. How do you find \( f(5) \) for the same function rule?
2. What is the general shape of the graph for this function?
3. How would \( f(x) \) change if the \( +10 \) term were removed?
4. How do you solve for \( f(x) = 0 \) in this equation?
5. What would happen to \( f(x) \) if you multiplied the entire equation by a constant?

**Tip:** Always calculate exponents before performing multiplication or addition in function rules!

Use the following function rule to find f(–4). f(x) = 2x + 2x^2 + 10. f(–4) =

Learn how to evaluate the polynomial function f(x) = 2x + 2x^2 + 10 at x = -4. This step-by-step solution explains the key concepts of algebra, function evaluation, and polynomial functions. Suitable for students in Grades 8-10.

Math Problem Statement

Solution

Ask a new question for Free

By Image

Math Problem Analysis

Mathematical Concepts

Formulas

Theorems

Suitable Grade Level

Related Recommendation