Question

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.