Convert the equation from vertex form to standard form y=−4(x+5)2−3 .

Answer 1

To convert the equation from vertex form to standard form, we start with the given vertex form equation:

\[ y = -4(x + 5)^2 - 3 \]

1. Expand the squared term: \[ (x + 5)^2 = x^2 + 10x + 25 \]

   Now substituting this back into the equation:

   \[ y = -4(x^2 + 10x + 25) - 3 \]

2. Distribute the -4: \[ y = -4x^2 - 40x - 100 - 3 \]

3. Combine like terms: \[ y = -4x^2 - 40x - 103 \]

Now, the equation in standard form (Ax^2 + Bx + C) is:

\[ y = -4x^2 - 40x - 103 \]

This is the standard form of the given equation.