Let's compute \( F(-1) \) given the function \( F(x) = 5x^2 - 10x + 21 \).

Given \( x = -1 \):
\[ F(-1) = 5(-1)^2 - 10(-1) + 21 \]

First, calculate \( (-1)^2 \):
\[ (-1)^2 = 1 \]

Next, substitute and compute:
\[ F(-1) = 5(1) - 10(-1) + 21 \]
\[ = 5 + 10 + 21 \]
\[ = 36 \]

Therefore, \( F(-1) = 36 \).

You're absolutely correct!

Given the function \( F(x) = 5x^2 - 10x + 21 \) and substituting \( x = -1 \), the steps follow:

1. Start with the function:
   \[
   F(-1) = 5(-1)^2 - 10(-1) + 21
   \]
   
2. Compute \( (-1)^2 = 1 \):
   \[
   F(-1) = 5(1) - 10(-1) + 21
   \]

3. Simplify:
   \[
   F(-1) = 5 + 10 + 21 = 36
   \]

Thus, \( F(-1) = 36 \).

Would you like to explore further or have any additional questions?

Here are 5 related questions:
1. What is the value of \( F(0) \) for the same function?
2. How does the derivative of \( F(x) \) look, and what does it tell us about the function?
3. What are the critical points of \( F(x) \)?
4. Can you find the roots of \( F(x) = 0 \)?
5. What happens to \( F(x) \) as \( x \to \infty \)?

**Tip:** When evaluating functions, always simplify exponents and negatives first to avoid mistakes.

Let's compute F(-1) given the function F(x) = 5x^2 - 10x + 21.

Calculate the value of the quadratic function F(x) = 5x^2 - 10x + 21 at x = -1 with a detailed step-by-step solution. This problem covers key algebraic concepts like substitution and function evaluation, suitable for students in Grades 7-9.

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