https://file.aiquickdraw.com/mathbot/file/1726787709186ur1hzw3h.jpg

The image contains several functions and prompts to evaluate them at specific values of \( x \). I'll break them down step-by-step for you:

### Functions and Evaluation Points:
1. \( f(x) = 2x + 11 \), evaluate for \( x = 10 \).
2. \( f(x) = -2x^2 + 4x - 7 \), evaluate for \( x = 2 \).
3. \( f(x) = 3x^2 + 5x - 1 \), evaluate for \( x = 2 \).
4. \( f(x) = 2k_2 + 5k_1 + 1 \), evaluate for \( k_1 = 1 \) and \( k_2 = 2 \).

Let me calculate the values of each function for the given \( x \) and \( k \) values.

### 1. \( f(x) = 2x + 11 \), for \( x = 10 \):
\[
f(10) = 2(10) + 11 = 20 + 11 = 31
\]

### 2. \( f(x) = -2x^2 + 4x - 7 \), for \( x = 2 \):
\[
f(2) = -2(2^2) + 4(2) - 7 = -2(4) + 8 - 7 = -8 + 8 - 7 = -7
\]

### 3. \( f(x) = 3x^2 + 5x - 1 \), for \( x = 2 \):
\[
f(2) = 3(2^2) + 5(2) - 1 = 3(4) + 10 - 1 = 12 + 10 - 1 = 21
\]

### 4. \( f(x) = 2k_2 + 5k_1 + 1 \), for \( k_1 = 1 \) and \( k_2 = 2 \):
\[
f(k_1, k_2) = 2(2) + 5(1) + 1 = 4 + 5 + 1 = 10
\]

These are the evaluated results for each function. Let me know if you need further clarification or have any additional questions!

Here are 5 related questions to further explore:
1. What is the derivative of each function?
2. How would you evaluate \( f(x) = 3x^2 + 5x - 1 \) for \( x = -2 \)?
3. Can you plot the function \( f(x) = -2x^2 + 4x - 7 \) for a range of \( x \)?
4. How does the evaluation change if you substitute \( x = -1 \) in \( f(x) = 2x + 11 \)?
5. What are the roots of the quadratic function \( f(x) = 3x^2 + 5x - 1 \)?

**Tip:** When dealing with quadratic functions, always remember the formula for finding the roots: \( x = \frac{-b \pm \sqrt{b^2 - 4ac}}{2a} \).

Evaluate the following functions: 1. f(x) = 2x + 11 for x = 10. 2. f(x) = -2x^2 + 4x - 7 for x = 2. 3. f(x) = 3x^2 + 5x - 1 for x = 2. 4. f(x) = 2k_2 + 5k_1 + 1 for k_1 = 1 and k_2 = 2.

Learn how to evaluate linear and quadratic functions for given values. This problem walks through solving f(x) = 2x + 11, f(x) = -2x^2 + 4x - 7, and more for specific values of x. Perfect for students in Grades 7-9.

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