To evaluate the expression \(3x^2 + 4x - 7\) at \(x = -3\), substitute \(-3\) for \(x\) in the equation:

\[
3(-3)^2 + 4(-3) - 7
\]

Now, calculate each term step by step:

1. Square \(-3\):
   \[
   (-3)^2 = 9
   \]

2. Multiply by 3:
   \[
   3 \times 9 = 27
   \]

3. Multiply 4 by \(-3\):
   \[
   4 \times (-3) = -12
   \]

4. Combine the terms:
   \[
   27 - 12 - 7 = 8
   \]

So, the value of the expression \(3x^2 + 4x - 7\) at \(x = -3\) is **8**.

Would you like any details on this calculation or have any questions?

Here are 5 related questions to explore further:
1. What is the value of \(3x^2 + 4x - 7\) at \(x = 2\)?
2. How do you find the roots of the quadratic equation \(3x^2 + 4x - 7 = 0\)?
3. What is the vertex of the parabola represented by \(y = 3x^2 + 4x - 7\)?
4. How does changing the coefficient of \(x^2\) affect the shape of the parabola?
5. What is the axis of symmetry for the parabola represented by \(y = 3x^2 + 4x - 7\)?

**Tip:** When evaluating a polynomial expression at a given value, substitute the value carefully and follow the order of operations (PEMDAS: Parentheses, Exponents, Multiplication and Division, Addition and Subtraction).

Learn how to evaluate the polynomial expression 3x^2 + 4x - 7 at x = -3 using substitution and order of operations. Understand the steps involved in calculating the value of this polynomial expression. Suitable for high school students.

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