To convert the equation \( y = -4(x + 5)^2 - 3 \) from vertex form to standard form, we'll need to expand it.
- Start by expanding the squared term:
\[ (x + 5)^2 = x^2 + 10x + 25 \]
- Substitute this back into the equation:
\[ y = -4(x^2 + 10x + 25) - 3 \]
- Distribute \(-4\):
\[ y = -4x^2 - 40x - 100 - 3 \]
- Combine like terms:
\[ y = -4x^2 - 40x - 103 \]
Thus, the standard form of the equation is:
\[ y = -4x^2 - 40x - 103 \]
So the correct response is:
y = -4x² - 40x - 103.