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.