Convert the equation from vertex form to standard form y=−4(x+5)2−3 .(1 point)

Question

Responses

y=16x2+160x+397
y equals 16 x squared plus 160 x plus 397

y=−4x2−40x−103
y equals negative 4 x squared minus 40 x minus 103

y=−4x2−25x−3
y equals negative 4 x squared minus 25 x minus 3

y=16x2+160x+412
y equals 16 x squared plus 160 x plus 412

Answer 1

To convert the equation from vertex form to standard form, let's start with the given equation:

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

1. First, expand the squared term:

\[ (x + 5)^2 = x^2 + 10x + 25. \]

2. Now substitute this back into the equation:

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

3. Distribute the -4:

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

4. Combine like terms:

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

Now, looking at the responses provided, the correct conversion from vertex form to standard form results in:

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

Thus, the correct answer is:

y = −4x² − 40x − 103.