To convert the equation from vertex form to standard form, we start with the given vertex form equation:
\[ y = -4(x + 5)^2 - 3 \]
We can expand this equation step by step.
-
First, expand the squared term: \[ (x + 5)^2 = x^2 + 10x + 25 \]
-
Substitute this back into the equation: \[ y = -4(x^2 + 10x + 25) - 3 \]
-
Distribute \(-4\) across the terms in the parentheses: \[ y = -4x^2 - 40x - 100 - 3 \]
-
Combine the constant terms: \[ y = -4x^2 - 40x - 103 \]
Thus, the standard form of the equation is:
\[ y = -4x^2 - 40x - 103 \]
From the given responses, the correct answer is:
y = −4x² − 40x − 103