Let's simplify the given function step by step.

The function is given as:

\[ f(7a) = -2(7a)^2 + 3(7a) \]

1. **Square the term \( (7a)^2 \):**

\[
(7a)^2 = 49a^2
\]

Now substitute this back into the equation:

\[
f(7a) = -2(49a^2) + 3(7a)
\]

2. **Simplify the terms:**

\[
f(7a) = -98a^2 + 21a
\]

So, the simplified form of the function is:

\[
f(7a) = -98a^2 + 21a
\]

Would you like more details on this, or have any further questions?

Here are 5 related questions:
1. How would you solve \( f(7) \) using this function?
2. What is the derivative of \( f(7a) = -98a^2 + 21a \)?
3. What is the maximum or minimum value of \( f(a) = -98a^2 + 21a \)?
4. How would the function change if the coefficient of \( a^2 \) was positive?
5. What happens if we set \( f(7a) = 0 \) and solve for \( a \)?

**Tip:** Always distribute carefully when simplifying expressions involving parentheses and exponents.

The query submitted by the user: f(7a) = −2(7a)^2 + 3(7a)

Discover how to simplify the quadratic function f(7a) = −2(7a)^2 + 3(7a) with step-by-step guidance. This problem covers key algebraic concepts, including function simplification and the quadratic equation. Suitable for students in Grades 8-10.

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