https://file.aiquickdraw.com/mathbot/file/1726065012215w6vchp1l.jpg

The expression to evaluate is:

\[
2x^2 + x + 6
\]

Let's evaluate it for the given values of \(x\).

### a. \( x = 3 \)

Substitute \(x = 3\) into the expression:
\[
2(3)^2 + 3 + 6 = 2(9) + 3 + 6 = 18 + 3 + 6 = 27
\]
So, for \( x = 3 \), the result is **27**.

### b. \( x = -2 \)

Substitute \(x = -2\) into the expression:
\[
2(-2)^2 + (-2) + 6 = 2(4) - 2 + 6 = 8 - 2 + 6 = 12
\]
So, for \( x = -2 \), the result is **12**.

### c. \( x = 0 \)

Substitute \(x = 0\) into the expression:
\[
2(0)^2 + 0 + 6 = 0 + 0 + 6 = 6
\]
So, for \( x = 0 \), the result is **6**.

### d. \( x = 5 \)

Substitute \(x = 5\) into the expression:
\[
2(5)^2 + 5 + 6 = 2(25) + 5 + 6 = 50 + 5 + 6 = 61
\]
So, for \( x = 5 \), the result is **61**.

### Summary of results:
- \( x = 3 \) → 27
- \( x = -2 \) → 12
- \( x = 0 \) → 6
- \( x = 5 \) → 61

Let me know if you'd like a more detailed explanation or have any questions!

### Related Questions:
1. How do you calculate the square of a negative number?
2. What changes in the equation if we add a coefficient to the \(x\) term?
3. How does the constant term (6) affect the output of the expression?
4. What happens when you substitute fractional or decimal values for \(x\)?
5. How would the results differ if the quadratic coefficient was negative?

**Tip:** Always remember to handle negative numbers carefully when squaring, as the result will be positive.

Evaluate the expression 2x^2 + x + 6 for the given values of x: x = 3, x = -2, x = 0, x = 5

Learn how to evaluate the quadratic expression 2x^2 + x + 6 for different values of x such as 3, -2, 0, and 5. This problem involves algebraic concepts including substitution and evaluating quadratic expressions, suitable for Grades 7-9 students.

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