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

Question

.(1 point)
Responses

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

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

Answer 1

To convert the equation \( y = -4(x + 5)^2 - 3 \) from vertex form to standard form, we'll need to expand it.

1. Start by expanding the squared term:

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

2. Substitute this back into the equation:

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

3. Distribute \(-4\):

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

4. Combine like terms:

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

Thus, the standard form of the equation is:

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

So the correct response is:

y = -4x² - 40x - 103.