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

Question

Responses

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

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

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

y=−4x2−40x−103

Answer 1

To convert the equation from vertex form \( y = -4(x + 5)^2 - 3 \) to standard form, we will expand the squared term and simplify the expression.

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

So, the standard form of the equation is: \[ y = -4x^2 - 40x - 103 \]

The correct response is: y = −4x² − 40x − 103.