Evaluate the expression:

x² - 3y + 12 if x = -2 and y = 5

To evaluate the expression \( x^2 - 3y + 12 \) given \( x = -2 \) and \( y = 5 \):

1. Substitute \( x = -2 \) and \( y = 5 \) into the expression:
   \[
   (-2)^2 - 3(5) + 12
   \]

2. Calculate \( (-2)^2 \):
   \[
   (-2)^2 = 4
   \]

3. Calculate \( -3(5) \):
   \[
   -3(5) = -15
   \]

4. Substitute the values back into the expression:
   \[
   4 - 15 + 12
   \]

5. Perform the addition and subtraction:
   \[
   4 - 15 = -11
   \]
   \[
   -11 + 12 = 1
   \]

So, the value of the expression is \( 1 \).

Would you like further details or have any questions? Here are five related questions:

1. What would the expression evaluate to if \( x = 3 \) and \( y = 4 \)?
2. How does the expression change if the coefficient of \( y \) is doubled?
3. What is the general form of the expression when expanded?
4. Can you find the roots of the expression \( x^2 - 3y + 12 = 0 \) for given \( y \) values?
5. How does changing the constant term (12) affect the outcome?

**Tip:** When evaluating expressions, always perform operations in the correct order: exponents first, then multiplication/division, and finally addition/subtraction.

Learn how to evaluate the expression x² - 3y + 12 with x = -2 and y = 5. This problem involves substituting values into a quadratic expression and performing arithmetic operations step-by-step. Suitable for students in Grades 7-9 studying algebraic expressions.

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