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.