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The image contains a problem asking for the value of the difference quotient \(\frac{f(a+h) - f(a)}{h}\) for a given function \(f(x)\).

### Problem Statement:
Given the function \(f(x) = x^2 - 5x + 2\), the task is to find the value of the difference quotient:
\[
\frac{f(a+h) - f(a)}{h}
\]
for \(a = 1\).

### Solution:
Let's go through the steps to solve the problem.

1. **Substitute the function \(f(x)\):**
   \[
   f(x) = x^2 - 5x + 2
   \]
   
2. **Find \(f(a)\):**
   Since \(a = 1\),
   \[
   f(1) = (1)^2 - 5(1) + 2 = 1 - 5 + 2 = -2
   \]

3. **Find \(f(a+h)\):**
   Substitute \(a + h\) into the function:
   \[
   f(1+h) = (1+h)^2 - 5(1+h) + 2
   \]
   Expand and simplify:
   \[
   f(1+h) = (1 + 2h + h^2) - (5 + 5h) + 2 = h^2 - 3h - 2
   \]

4. **Calculate the difference \(f(a+h) - f(a)\):**
   \[
   f(1+h) - f(1) = (h^2 - 3h - 2) - (-2) = h^2 - 3h
   \]

5. **Find the difference quotient:**
   \[
   \frac{f(a+h) - f(a)}{h} = \frac{h^2 - 3h}{h} = h - 3
   \]

So, the difference quotient simplifies to \(h - 3\).

Given the specific options provided in the image (though not clearly visible, the final solution's simplified form should match one of them), the difference quotient is likely \(h - 3\).

Would you like further details or explanations on any of the steps? Here are five additional questions you might find helpful:

1. How is the difference quotient related to the derivative?
2. What happens to the difference quotient as \(h\) approaches 0?
3. Can the difference quotient be used to find the slope of a tangent line?
4. What is the geometric interpretation of the function \(f(x)\)?
5. How does changing the value of \(a\) affect the difference quotient?

**Tip:** The difference quotient is a fundamental concept in calculus, as it forms the basis for understanding derivatives.

For the function f(x) = x^2 - 5x + 2, find the value of the difference quotient \(\frac{f(a+h) - f(a)}{h}\) for a = 1.

Learn how to calculate the difference quotient for the function f(x) = x^2 - 5x + 2, with a detailed step-by-step solution. This problem covers key algebraic concepts, including the difference quotient and quadratic functions. Suitable for students in Grades 9-11.

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