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

Question

.(1 point)
Responses

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

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

y=−4x2−40x−103

Answer 1

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

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

We need to expand this:

1. First, expand \((x + 5)^2\):

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

2. Now substitute this back into the equation:

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

3. Distribute \(-4\):

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

4. Combine the constants:

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

So the equation in standard form is:

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

The correct response is:

y = −4x² − 40x − 103.