Answer :
We are given the function
$$
f(x) = -9(x+5)^2 + 4.
$$
Our goal is to convert it into standard form, that is
$$
f(x) = ax^2 + bx + c.
$$
**Step 1. Expand the square**
First, expand the binomial:
$$
(x+5)^2 = x^2 + 2\cdot5\cdot x + 5^2 = x^2 + 10x + 25.
$$
**Step 2. Distribute the coefficient**
Multiply the expanded form by $-9$:
$$
-9(x^2 + 10x + 25) = -9x^2 - 90x - 225.
$$
**Step 3. Add the constant**
Now, add the constant $+4$:
$$
-9x^2 - 90x - 225 + 4 = -9x^2 - 90x - 221.
$$
Thus, the standard form of the function is:
$$
f(x) = -9x^2 - 90x - 221.
$$
This corresponds to the correct answer.
$$
f(x) = -9(x+5)^2 + 4.
$$
Our goal is to convert it into standard form, that is
$$
f(x) = ax^2 + bx + c.
$$
**Step 1. Expand the square**
First, expand the binomial:
$$
(x+5)^2 = x^2 + 2\cdot5\cdot x + 5^2 = x^2 + 10x + 25.
$$
**Step 2. Distribute the coefficient**
Multiply the expanded form by $-9$:
$$
-9(x^2 + 10x + 25) = -9x^2 - 90x - 225.
$$
**Step 3. Add the constant**
Now, add the constant $+4$:
$$
-9x^2 - 90x - 225 + 4 = -9x^2 - 90x - 221.
$$
Thus, the standard form of the function is:
$$
f(x) = -9x^2 - 90x - 221.
$$
This corresponds to the correct answer.
