Evaluate
f
(
x
−
4
)
f
(
x
-
4
)
for the function
f
(
x
)
=
x
2
−
3
x
f
(
x
)
=
x
2
-
3
x

Given the function \( f(x) = x^2 - 3x \), we are asked to evaluate \( f(x - 4) \).

### Step 1: Substitute \( x - 4 \) into the function

To find \( f(x - 4) \), substitute \( x - 4 \) for \( x \) in the expression for \( f(x) \):

\[
f(x - 4) = (x - 4)^2 - 3(x - 4)
\]

### Step 2: Expand \( (x - 4)^2 \) and simplify

First, expand the square:
\[
(x - 4)^2 = x^2 - 8x + 16
\]

Now, distribute the -3 over \( (x - 4) \):
\[
-3(x - 4) = -3x + 12
\]

### Step 3: Combine all terms

Now combine the two expressions:
\[
f(x - 4) = (x^2 - 8x + 16) + (-3x + 12)
\]
Simplify by combining like terms:
\[
f(x - 4) = x^2 - 11x + 28
\]

### Final Answer:
\[
f(x - 4) = x^2 - 11x + 28
\]

Do you need further details or explanations?

Here are 5 related questions for practice:
1. What is \( f(x + 3) \) for the function \( f(x) = x^2 - 3x \)?
2. How would you solve \( f(2) \) for the same function?
3. How do you find the vertex of the quadratic function \( f(x) = x^2 - 11x + 28 \)?
4. What are the roots of \( f(x - 4) = 0 \)?
5. How would you differentiate \( f(x) = x^2 - 3x \)?

**Tip:** When substituting into functions, simplify expressions step by step to avoid errors.

Evaluate f(x - 4) for the function f(x) = x^2 - 3x

Learn how to evaluate f(x - 4) for the quadratic function f(x) = x^2 - 3x. This step-by-step solution guides you through function substitution, expanding binomials, and simplifying expressions. Perfect for students in Grades 8-10 learning quadratic functions and algebraic techniques.

Math Problem Statement

Evaluate f ( x − 4 ) f ( x

4 ) for the function f ( x )

x 2 − 3 x f ( x )

x 2

Solution

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