Question

convert the equation from vertex form to standard for y = -4(x+5)^2 - 3
a y = 16x^2 + 160x + 412
b y = -4x^2 - 25x - 3
c y = -4x^2 - 40x - 103
d y = 16x^2 + 160x + 397

Answer 1

To convert the equation from vertex form \( y = -4(x + 5)^2 - 3 \) into standard form, we will expand the equation.

1. **Start with the vertex form:**
\[
y = -4(x + 5)^2 - 3
\]

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

3. **Substitute this back into the equation:**
\[
y = -4(x^2 + 10x + 25) - 3
\]

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

5. **Combine the constant terms:**
\[
y = -4x^2 - 40x - 103
\]

Now that we have the equation in standard form, we can compare it with the provided options:

c) \( y = -4x^2 - 40x - 103 \)

Thus, the correct answer is:

**c) \( y = -4x^2 - 40x - 103 \)**.